The Palestinian group Hamas has sent a letter addressed to the US president via a US politician visiting Gaza, a senior UN official has said.
UN relief agency chief Karen Abu Zayd told the BBC the letter had been received by the UN and passed on.
She did not say if Senator John Kerry had accepted it, and there were no details about the letter's contents.
The US views Hamas, which seized control of Gaza in 2007, as a terrorist organisation and will not deal with it.
A former presidential candidate, Mr Kerry was visiting Gaza with US congressmen Brian Baird and Keith Ellison in the first such visit to the Hamas-run Strip since 2007.
The men are not likely to meet Hamas.
Correspondents say their visit appears to be more humanitarian than political.
As the head of the Senate Foreign Committee, Mr Kerry is a senior Democrat, but all three men are visiting Gaza in their capacity as lawmakers, not representatives of the administration of President Barack Obama.
A spokeswoman for the US consulate said it was thought to be the first visit by US congressmen for at least four years.
Mr Kerry also visited the Israeli town of Sderot, a target of Palestinian rocket attacks, before entering Gaza.
Standing in front of a pile of used rockets, Mr Kerry said that both he and President Obama believed that nobody should have to spend their lives in fear of attack.
"I know that our president, President Obama, whom I support strongly, stood right here," he said, referring to a visit before the 2008 US election.
"He was right here in front of these rockets. He came to Sderot as I have because we feel very deeply that no-one should live under this kind of threat, no children should be raised in that kind of fear.
"We are sympathetic with the crisis that people face on a daily basis here in Israel, from those who choose no other path other than to use instruments of terror."
Earlier he said: "[The visit] does not indicate any shift whatsoever with respect to Hamas... what it indicates is our effort to listen and to learn."
Hamas won elections in 2006 and consolidated control by force in 2007.
Like Israel, the EU and the UN, the US government officials refuse to deal with the militant group.
In addition, there have been security concerns since Palestinian militants blew up an American diplomatic convoy in October 2003, killing three people.
Mr Ellison, from Minnesota, was the first Muslim elected to the US Congress, while Mr Baird, a clinical psychologist, is from Washington.
Rockets fired
Their visit came as violent incidents tested the unilateral ceasefires Israel and Hamas have both declared, amid Egyptian-brokered attempts to reach a firmer truce deal.
The Israeli military confirmed it was carrying out airstrikes in the Gaza Strip, but gave no further details.
This followed the launching of two rockets from Gaza into Israel on Thursday morning, after two mortars were fired the previous night.
The Israeli military said its forces had also crossed into Gaza and shot and lightly injured a Palestinian near the border fence, after the man's behaviour raised suspicions he was attempting to plant a bomb.
About 1,300 Palestinians and 13 Israelis died during Israel's three-week operation in January, which was aimed at halting Palestinian rocket fire into Israel.
Since Israel withdrew its forces from Gaza, sporadic rocket and mortar fire has continued, while Israel has carried out several airstrikes against smuggling tunnels in the south of Gaza, and what it says are militant facilities elsewhere in the territory.
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