He seemed to come from nowhere, walking at a fast pace across the junction where we were parked in the heart of the crowded refugee camp. Alerted to the registration number of our taxi, he opened a back door and slipped into the rear seat. "Let's get out of here," he said. "There are eyes everywhere."

This sounds melodramatic, but it may also be understandable. A militant since the beginning of the second intifada, he is wanted by Israel, and therefore identifiable from an overhead drone, like the one which, three days after we spoke, destroyed a Subaru, killing its occupants, two brothers from the Army of Islam, the extremist Islamist organisation that kidnapped the BBC correspondent Alan Johnston in 2007.

But this good-looking Palestinian in his thirties says it is not the Israeli military that has made him nervous about talking to us. Rather it's the internal security force of Hamas, whose plain-clothes operatives arrested him this year while he was leading a group of fighters intending to mount what he will only delicately describe as a military "operation" against Israel. Before speaking to us, he extracted a promise not to use his name or identify his faction, the month he was detained, or even the area of Gaza he was arrested in, or the exact nature of the "operation" he'd been part of.

While in detention, he was beaten with fists and rifle butts. "They said to me: 'You're trying to make an operation. This is forbidden. There is a hudna [truce]. We have no resistance here. Gaza has been liberated. If you want to do an operation, do it in the West Bank, or in 1948 territory [Israel].' We said: 'As long as there is an occupation, we have to fight and no one should stop us.' This is not the Hamas we know from before the elections. It is completely different. They are always in border areas, telling people don't get close to the border. They used to be with the resistance, but once you get into authority you change. They want to protect their authority and they fear that there is going to be a war."

What makes us as confident as we can be that he's genuine is not so much the way he lowers his voice and suddenly stops talking altogether when the waiter brings us coffee in the quiet sunlit garden of a Gaza City hotel, but that we were pointed towards him by a reputable and independent Palestinian NGO. Assuming our confidence is justified, what he had to say is persuasive testimony that Hamas not only agreed to a Gaza ceasefire in the aftermath of Operation Cast Lead (Israel's military onslaught in the winter of 2008-09), but is enforcing it. And this may pose some intriguing policy questions for Israel and the international community when the US is still struggling to bring Benjamin Netanyahu's government, together with the moderate Palestinian leadership headed by President Mahmoud Abbas, into direct talks which would exclude the Islamic faction. Should this even be the moment to contemplate lifting the international boycott on all contacts with Hamas?

According to one independent estimate, in the past two months, between 25 and 30 people have been detained by Gazan security forces for seeking to launch attacks on Israel. On a daytime trip down Gaza's eastern road, parallel to the Israeli border, you come across the occasional post manned by men from the green-uniformed Hamas national security force. But observers say that at night they often lie in wait within 700m of the border fence ready to pounce on those wanting to fire rockets at Israel. Either way, in 2007, according to Israeli figures, 2,433 rockets and mortars were fired into Israel from Gaza; in 2008, 3,278; in 2009, 774, the large majority during the Israeli onslaught on Gaza which ended in January. So far this year, it has been about 180.

The slowdown has not been stable. In the run-up to President Barack Obama's Washington meeting with Netanyahu and Abbas in early September, four Israeli settlers were killed by Hamas gunmen in the West Bank. And, as the now stalled direct negotiations began, there was a sharp temporary rise in rocket and mortar attacks from Gaza – a reminder of Hamas's capacity to undermine such negotiations if it chooses. There was a spike 10 days ago when Qassam rockets, mortars and one Russian-made Grad were fired at Israel in response to the killing of the two brothers from the Army of Islam.

Even that brief barrage was instructive. The attacks – some claimed by another smaller faction, the Popular Resistance Committees – came from an area regarded as well controlled by the Hamas security forces. It's assumed therefore that Hamas, for whom the Army of Islam has proved one of the most troublesome factions, and which has been taunted from time to time on pro-opposition websites for abandoning armed "resistance", decided to turn a blind eye to the Friday launches. Yet they ended almost as quickly as they had started, reportedly after a meeting Hamas held the next day with the main factions, and despite a series of incursions over the next few days by the Israeli military into the Palestinian side of the border. These are broadly of a kind Israel's army routinely makes to enforce a "buffer zone" inside Gaza; sometimes these are confronted with retaliatory machine gun or mortar fire but significantly more rarely on targets where civilian Israeli death or injury is likely.

At the end of October, Mahmoud al-Zahar, Hamas's main political leader in Gaza, was reported in the Arabic daily Al Hayat to have described as "rebels" those who launched rockets at Israel. "Did we agree to the truce in order to stick to it, or to violate it?" the paper quoted him as saying. At his home a fortnight later, Zahar shrugged off the Al Hayat report as unreliable, insisting that the main purpose of Hamas's security presence in border areas was for defence against Israel and the identification and detention of "collaborators". But he also confirmed that Hamas had agreed with Egypt after the 2008-09 war to a ceasefire, and there was therefore no "new policy". He added: "We are putting one condition: if Israel looks for a ceasefire we are looking for a ceasefire; if Israel is going to attack, we have to respond."

The restraint no doubt testifies to the deterrent impact of Israel's 2008-09 onslaught. But Israel's future policy towards Gaza and Hamas is much less clear. In a briefing this month, a high-ranking Israeli intelligence official suggested that a second war would be necessary to eliminate the military threat from Hamas and begin a process of restoring control of Gaza to the Abbas leadership.

A leading Israeli analyst, Yossi Alpher, believes such a course would be "disastrous", estimating the price might be the lives of 200 Israeli soldiers. " Is the Israeli public prepared to pay that price?" says Alpher. "I am not sure it is." Moreover, regime change engineered by an Israeli war would in his view turn the Abbas leadership into "Quislings" in the eyes of the Gazan public. Israel's record of trying to impose amenable Palestinian leadership is not encouraging, he says. "We don't do this well. We screw up." And he warns that the status quo is "unsustainable", that there has been no response to Hamas's present restraint "at anything but the military level" and that "we do not have a strategy for dealing with Hamas". Alpher acknowledges the complicating factor that the US, Egypt and the moderate Palestinian leadership do not want Israel to negotiate with Hamas. Alpher who has long argued that the blockade of Gaza is “counterproductive”, says that by easing it this year for consumer goods Netanyahu has disposed of the argument that Hamas’s incarceration of the Israeli soldier Gilad Shalit is an obstacle to a much wider loosening, both for imports and exports. But he also suggests that if direct peace negotiations get under way, Israel should “look for an opening” in co-ordination with the moderate Palestinian leadership for talks with Hamas not only on Shalit but to “institutionalise the ceasefire” -- if only to prevent Hamas sabotaging progress.

Another Israeli expert, Ephraim Halevy, a former Mossad chief, agrees about the unsustainability of the status quo in Gaza. But Halevy, who is deeply sceptical about the ability of Israel and the Abbas leadership to implement a peace agreement, has long believed that Israel should go even further in talks with Hamas and test the Islamic faction's claims that it would agree to a hudna of many years in return for a Palestinian state on 1967 borders. Halevy adds: "There is no point in institutionalising the ceasefire unless you also engage with Hamas on a political level."

Either way, there is a contradiction not lost on some officials in parts of the Middle East Quartet: the US, the EU, Russia and the UN. "It's odd that Quartet contacts with Hamas are completely taboo," says a Western diplomat, "when we can think about talking to the Taliban."