Jimmy Carter, a former US president, has met Khaled Meshaal, the exiled Hamas leader, in the Syrian capital, despite opposition from Tel Aviv and Washington.
The meeting on Friday is said to have addressed Hamas rocket attacks on Israel and prospects for the release of Palestinians held in Israeli jails.
"Carter suggested a truce and that Hamas should stop its rockets against Israel," Mohammed Nazzal, a Hamas leader, said after the five-hour meeting with the former president in Damascus.
"We support a truce, but Israel should support it too," he said.
An Israeli economic siege on Gaza and a proposal by an Israeli minister to meet Hamas to discuss the fate of an Israeli soldier held by the Palestinians was also covered in Damascus.
David Foley, the US State Department spokesman for Near East Affairs, told Al Jazeera that Carter "does not have the support of the US government".
"We've been very clear about our position about Jimmy Carter. Former President Carter is a private citizen and is on a private visit," he said.
Al Jazeera's Clayton Swisher reported that Carter's talks with Meshaal were conducted in a "pleasant" atmosphere.
"Al Jazeera has learned, based on exclusive sources inside the Carter-Hamas talks, that a delegation of Hamas officials from the Gaza Strip, led by the Hamas foreign minister Mahmoud Zahar, is going to arrive in Damascus on Saturday to join the talks with President Carter and Hamas leadership," he said.
Carter arrived in Syria on Friday and held talks with Bashar al-Assad, the Syrian president, before meeting Meshaal.
Details on the meeting with al-Assad were not immediately available, but Rick Jafculca, Carter's spokesman, said that the two men had been due to discuss the peace process.
In the run up to the meeting, Israel's deputy prime minister was reported to have told Carter that he is ready to meet Meshaal to negotiate the release of prisoners held by Hamas.
Haaretz daily newspaper quoted Eli Yishai as saying: "I am ready to meet with all necessary Hamas members."
However, Carter's meeting with Hamas has been criticised by the US and Israel.
Hamas is listed as a terrorist organisation by Washington, Tel Aviv and the EU, and has not been invited to participate in US-brokered peace negotiations between Israel and the Palestinians.
On the possibility of considering Hamas as peace partner, Foley said: "We want to see Hamas part of the peace process, to be a partner for peace with the Israelis that will lead to two states side by side living in peace and security.
"We need to see Hamas simply do a couple of things first and that will show that they are actually serious about peace."
But Fawaz Gerges, chair of Middle East and International Affairs at Sarah Lawrence College in New York, said Carter had set a precedent.
"He has broken the ice. One would hope that not only Israeli leaders but world leaders and the next president of the United States would engage Hamas diplomatically," he said.
"As Carter said today, there is no way out of engaging with Hamas - it is the elected representative government of the Palestinian people."
Earlier on Friday, Hamas said Gilad Shalit, the Israeli soldier captured by fighters in the Gaza Strip, would "not see the light" until Palestinian prisoners were released in a prisoner exchange.
Mushir al-Masri, a Hamas official, said in a speech in Gaza: "Gilad will not see the light, will not see his mother, will not see his father, God willing, as long as our heroic prisoners do not see their families, in their houses."
Israel has agreed to release some inmates, but has balked at some of those on Hamas' list.
Carter had met a Hamas delegation in Cairo on Thursday, as well as Husni Mubarak, the Egyptian president.
Carter defended his meetings, calling them necessary in the Israeli-Palestinian peace process. He described Israel's siege of the Gaza Strip as a crime.
He said Palestinians in Gaza were being "starved to death", receiving fewer calories a day than people in the poorest parts of Africa.
Carter said that US attempts to undermine Hamas, democratically elected into power in January 2006, have been counterproductive.
In Moscow, Vladimir Putin, the Russian president, met Mahmoud Abbas, the Palestinian president and leader of Hamas' rival Fatah faction, to discuss plans for a Middle East peace conference.
Abbas, left, wants Russia to play a greater role
in the Middle East peace process [Reuters]
A Kremlin official told journalists that "special attention will be paid to ... possible steps by Russia, including its initiative to hold a Moscow meeting on the Middle East".
The official said Putin and Abbas would discuss how to stabilise the situation and restore Palestinian unity.
The US welcomed the Russian engagement. Foley told Al Jazeera: "Russia is a very valued member of the Quartet. They've been part of these [peace] discussions. Certainly we will welcome Russian engagement."
Israel has sealed off the West Bank and Gaza for 10 days as it celebrates the Jewish holiday of Passover.
Tanks moved into position at the crossings as the shutdown took effect early on Friday, barring Palestinians in the occupied territories from entering Israel.
The shutdown follows a statement by Hamas that "all options are open" to avenge the killing of 20 Palestinians in a day of air assaults and ground battles in Gaza that also left three Israeli soldiers dead.
In a statement published on the internet, the armed wing of Hamas called on its fighters to attack Israel "in every place and with all means available".
"This enemy only understands the language of force," it said.
The Israeli military said it would try its best to preserve the daily life of Palestinians, allowing humanitarian cases, doctors and lawyers to cross the border.
But Israel has already been restricting the flow of food and fuel supplies since Hamas seized control of the Gaza Strip last June.
Israel says the restrictions are in response to rocket attacks launched from there, but human rights groups argue that the siege is collective punishment of the populace.