Former US President Jimmy Carter set out plans for a ceasefire between Hamas and Israel at a meeting with Hamas leader Khaled Meshaal on Friday.

Carter held more than four hours of talks with Meshaal on Friday in one of the highest-profile meetings between the Islamist group that rules Gaza and a Western figure.

His aides planned to return for further talks with Hamas officials on Friday night, senior Hamas figure Mohammad Nazzal said. Carter's willingness to meet Hamas officials has drawn criticism from Israel and the United States.

The second round of talks would discuss details of proposals put forward by Carter and also examine the issue of the release of an Israeli soldier held by Hamas.

Hamas was open to the release of the soldier, Gilad Shalit, "but not without a price", Nazzal said. Hamas has previously demanded Israel free hundreds of jailed Palestinians in return for his release.

Nazaal said the discussions with Carter's advisers would  focus on the "price and mechanism" for releasing Shalit.

He added that the Carter-Meshaal meeting had discussed important issues, but details were left to their aides to hammer out. Hamas's leadership would need a few days to reach a position on the main issues of Shalit, a truce, and control of crossing points linking Gaza to the outside world.

"This meeting was not a courtesy call, concrete proposals were discussed and we admire Carter for making this effort. The discussions were frank and direct," Nazzal said.

Egypt said on Friday it was making good progress trying to negotiate a tacit ceasefire, including a prisoner exchange, between Israel and Hamas.

Speaking in Washington, Egyptian Foreign Minister Ahmed Aboul Gheit said his government was speaking with both sides to get a "period of quiet," which would help Israeli and Palestinian negotiators to more easily reach a deal in US-mediated Palestinian statehood talks that exclude Hamas.

Carter, 83, brokered the 1979 peace treaty between Israel and Egypt when he was president. He is on a Middle East tour to hear views on solving the Palestinian-Israeli conflict, and earlier met Syrian President Bashar al-Assad.

Israeli Prime Minister Ehud Olmert did not meet Carter during his visit to Israel this week and Washington has criticised him for his contacts with Hamas, which both the United States and Israel regard as a terrorist group.

Previous efforts by Egypt to broker a prisoner exchange deal between Hamas, whose charter calls for the Jewish state's demise, and Israel involving Shalit, captured by Palestinian fighters in a 2006 raid on Israeli territory, have foundered.

Hamas officials said they preferred to negotiate a prisoner exchange deal through a third party, not directly with Israeli officials.

In a proposal passed to Carter this week, an Israeli cabinet minister offered to meet the leadership of Hamas to ask for the release of the soldier -- a move which would contravene official Israeli government policy.

Carter met two senior Hamas officials in Cairo on Thursday after Israel refused him permission to enter the Gaza Strip, where they live. The two would now come to Damascus for talks with the Hamas leadership, Nazzal said.

Hamas, which is locked in a power struggle with Western-backed Palestinian President Mahmoud Abbas, has offered Israel a conditional truce. The Olmert government has written this off as a ruse that would allow Hamas to rearm and regroup. - Reuters