Former U.S. President Jimmy Carter arrived in Jordan Sunday to meet with King Abdullah.
Mr. Carter's visit follows meetings Friday and Saturday in Damascus, Syria, with exiled Hamas leader Khaled Meshaal. The former president has not commented on the talks.
A Hamas official, Mohammad Nazzal, told reporters Mr. Carter proposed a ceasefire between Israeli forces and Hamas fighters, a prisoner exchange, that would include kidnapped Israeli soldier Gilad Shalit and the lifting of Israel's blockade of the Gaza Strip.
The official said Hamas would respond soon.
Israel and the United States have criticized Mr. Carter for agreeing to meet with leaders of Hamas, which both countries consider a terrorist group.
But Mr. Carter says peace in Israel is impossible without engaging Hamas. In January 2006, the militant group won parliamentary elections in the Palestinian territories.
Mr. Carter mediated the 1978 Camp David Accords, which paved the way for peace between Israel and Egypt. He has taken positions critical of Israel in recent years. In a 2006 book, he described Israeli policies in the Palestinian territories as a "system of apartheid."
On Friday, Egypt's foreign minister Ahmed Aboul Gheit acknowledged that Egypt is quietly mediating talks between Israel and Hamas. He said the parties involved are "making good progress."
Some information for this report was provided by AP.