Tony Blair made a strong case yesterday for why it might be possible for outside brokers — such as himself — to lessen the damage done by the Israeli-Palestinian deadlock, even if they cannot yet resolve it. Speaking to a House of Commons committee, with many references to Northern Ireland (and, he might have added, to his creation of new Labour) he clearly drew on his belief in his personal ability to bridge incompatible positions.

It's easy, after Iraq, to recoil from his self-belief: that with a direct gaze, leaning across a table, he can bring enemies together. He overstates the parallels with Northern Ireland. He put a lot of weight on the unknown future: the next American president, the next Israeli prime minister, the reaction of the militant Islamic Hamas to events yet to unfold. But his account's strength lay in not pretending to influence more than a sliver of the picture. In recommending tiny steps and low expectations, he struck the right tone (and Barack Obama has shown, in this week's abrupt pro-Israel gesture, how to get it wrong).

After nearly a year of Blair's absence from the British stage, it is easy to forget the expansive familiarity that wrongfoots fans and critics. “How are you guys doing?,” he said, settling in before the Commons International Development Select Committee, as a tanned traveller dropping in on his old home town; their questions, in comparison, were dry, tangled and deferential. Gesturing with fingers pressed into a tent — the universal mannerism, it seems, of those who pronounce on the Middle East — he expanded on the deal he struck last month as the envoy of the Quartet (the US, EU, Russia and United Nations).

The scheme lifts some West Bank checkpoints to help the economy, while demanding Palestinian security improvements, but the changes had not yet happened, he acknowledged. And he cautioned that the crisis in Gaza, blockaded by Israel in retaliation for rocket attacks, “could overwhelm everything . . . the current situation won't hold and isn't acceptable”.

But Northern Ireland showed that “if you get some normality and calm, everything becomes possible”. He cited, as any optimist does, the support of most Israelis and Palestinians for a two-state solution, and added that “if the only alternative . . . is a one-state solution, then there's going to be a hell of a fight”.

His old skill in professing understanding of each side has been put to good use. To those who want talks with Hamas even though it does not recognise Israel, he said: “I totally understand people who say that [although] it's not the Quartet's position” while adding that “you can't dispute that Hamas has a military grip on Gaza and if they wanted to stop these [rocket] attacks they could”. He spent much time asserting impartiality, noting: “I've come to realise that what each side says about the other is essentially true.” He did argue that Israel “has to go farther and faster, especially on the West Bank”, and that some of its settlements “are illegal under Israeli law, never mind international law”, but did not mention its recent decision to expand them.

He said that “there will a real problem if a new American president takes a couple of years” to focus on the problem, which, he argued, was “fundamental to security in the region and to peace between Islam and the West”. Iraq may have compromised his own ability to make that case, one MP suggested yesterday. But still, he made a good case that his time in Bethlehem hotels counting tourists has not been wasted, and that there are parts of the deadlock that are susceptible to the talking cure.