Palestinian Prime Minister Ismail Haniya of the ruling Islamist Hamas movement confirmed reports that Egypt was mediating talks on a prisoner swap between Israel and armed groups in Gaza who seized the soldier.
"The Egyptians are making a lot of efforts. There are certain things going on to solve this question but there is nothing specific," Haniya said during a visit to a school in Gaza. "We hope the Egyptian efforts succeed," he added.
Hamas's armed wing was one of the three groups in Gaza to have claimed responsibility for the June 25 cross-border raid in which two soldiers were killed and a third, Corporal Gilad Shalit, captured.
Newspaper report
One of Israel's major newspapers, the Yediot Aharonot daily, said that under secret talks brokered by Egypt, Israel could release up to 800 Palestinian prisoners in return for Corporal Shalit, who turned 20 last Monday while still in captivity.
Quoting unnamed security officials, the paper said Israel would free the prisoners in three stages but that the talks were being held up by questions related to the timetable.
Israel has refused, however, to release Marwan Barghuti, a leader of the Palestinian uprising and a senior figure in president Mahmud Abbas's Fatah faction, Yediot said.
Top-level Israeli envoy Ofer Dekel was recently dispatched to Cairo by Prime Minister Ehud Olmert to discuss Shalit's release, Israeli public radio said Sunday.
Mr Olmert's spokeswoman Miri Eisen refused to confirm or deny the report, repeating only Israel's official position that it "does not negotiate with terrorists".
Corporal Shalit's father, Noam, also told AFP that talks over his son's release were underway.
"There are indirect contacts by Egyptian intermediaries. For the moment there is no progress, but I hope there will be some soon. That would be normal, after 70 days," the length of time his son has been missing.
"I have periodic contacts with the Palestinians in the Gaza Strip, but for the moment I haven't any and I think Hamas's political arm in Damascus holds the key to the situation."
Islamist warning
Meanwhile in a statement posted on an Islamist website the group that kidnapped two Fox News television journalists in Gaza has threatened to kill non-Muslims visiting the Palestinian territories unless at least one of its demands is met.
"For us, (taking) the blood of every infidel who comes to Palestine without having first converted to Islam is lawful," said the group calling itself the Holy Jihad Brigades.
The group threatened to kill anyone not converting to Islam, not paying a ransom or if Muslim prisoners held in Israel are not freed in exchange.
"We will face four choices: Islam, death, ransom or Muslim prisoners being freed"," said the statement.
The previously unheard of group abducted Fox News journalist Steve Centanni, a US national, and New Zealand cameraman Olaf Wiig on August 14. They were freed on August 27.