WASHINGTON - Egypt said on Friday it was making good progress trying to negotiate a tacit cease-fire, including a prisoner exchange, between Israel and the militant Palestinian group Hamas that controls the Gaza Strip.

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 achieve a deal more easily in U.S.-mediated Palestinian statehood talks that exclude Hamas.

"Hamas wants to call it a period of quiet. That suits the Israelis because they do not want to reach a signed, written agreement with Hamas," Gheit said of Egypt's mediation attempts in a speech to the Council on Foreign Relations in Washington.

"We are making good progress [mediating] but the difficulty we face is that often, certain trends inside Israel challenge the idea and certain trends inside Gaza challenge the idea and maybe, maybe there could also be a foreign element," he said with a smile, referring to the United States.

Israel and the United States both classify Hamas as a terrorist organization and shun contacts with it, although Washington has quietly given a nod for Egypt to negotiate with the Islamist group to end violence that threatens the statehood talks.

Outlining three elements of Egypt's mediation plan, Gheit said Hamas must cease firing missiles from Gaza into Israel. The Israelis, in turn, would vow not to target Palestinian activists inside Gaza and stop "targeted killings, assassinations or what have you."

The second element was a prisoner swap of about 400 Palestinians held by Israel in exchange for Israel Defense Forces soldier Gilad Shalit, said Gheit. Shalit was abducted in June 2006 and taken to the Gaza Strip.

Prime Minister Ehud Olmert has balked at the scope of the prisoner release roster.

Gheit said the plan was for Shalit to be delivered to the Egyptians, who in turn would hand him over to the Israelis.

"Our information is that he is still alive," said Gheit of the Israeli soldier, without providing further details.

The third element is to allow border crossings between Gaza and Israel to be open, with the help of European observers.

"If the crossings are to be open, then we would ensure that the flow of goods, of people, of material and of everything is allowed and the Palestinians in Gaza will not feel deprived as they are right now," he said.

The peace talks only involve the Wester-backed Palestinian President Mahmoud Abbas and Olmert. Gheit said if they reached a deal, which Washington wants by the end of the Bush administration's term in January 2009, then Hamas would be under pressure to accept it.

"I think over time, Hamas will have to change because by not changing they are damaging prospects for Palestinian peace," said Gheit, who also questioned whether Israel was committed to reaching a final settlement with the Palestinians.

Former U.S. President Jimmy Carter set out plans for a cease-fire between Hamas and Israel during a meeting with Hamas leader Khaled Meshal in Syria on Friday.

Gheit did not mention Carter's meeting with the Hamas leader. The Bush administration strongly opposed Carter's talks with Hamas and had advised him against it.