A senior Palestinian official has said militant groups have agreed to suspend their attacks on Israel and are now waiting for Israel's response.
Abbas wants a unified Palestinian stance in talks with Israel
It follows a week of talks between Palestinian leader Mahmoud Abbas and militants aimed at ending the violence.
The militant groups insist they will not actually announce a ceasefire unless Israel makes concessions on halting military operations.
Israel has said its armed forces will hold fire if calm prevails.
Mr Abbas said on Sunday that talks with the factions had made "great progress".
Meanwhile Israel, he said, had to "put a stop to the incursions and the attacks and other violent acts".
Anti-Israeli violence has dropped sharply since talks began between the Palestinian leader and militant groups.
Palestinian negotiator Ziad Abu Amr, speaking on Voice of Palestine radio on Monday, said the armed groups had promised to suspend attacks on Israel.
"They will continue doing that for some time to see if Israel is ready to accept demands and hold the truce," he said.
Mr Abbas, also known as Abu Mazen, has held five days of talks with the various Palestinian armed factions - known as the national dialogue - aimed at ending the violence.
In an interview with Palestinian television on Sunday he said "everybody feels the responsibility, and feels the need to put a stop to this situation we are living in".
"From this standpoint, we can say that the dialogue has advanced a great deal, and the differences have shrunk in a large way, and therefore I can say that we are bound to reach an agreement in the very near future."
Earlier, Hamas spokesman Abu Zuhri denied comments by Israeli Defence Minister Shaul Mofaz that both Hamas and Islamic Jihad had agreed to suspend attacks against Israel for a month.
Hamas says calm must come "with a price"
Mr Zuhri said there would be "no calm without a price and a calm will not be accepted unless there is a clear commitment from the occupation to stop all sorts of aggression".
Mr Mofaz told Israeli Radio that Hamas and Islamic Jihad had been promised a role in the Palestinian Authority by Mr Abbas in return for stopping the attacks.
He said Israel was willing to suspend operations against Palestinian militants but only if they did not carry out attacks.
His comments were echoed later by Prime Minister Ariel Sharon, who said there was now "quiet "after a period of "intensive action on the part of our security forces against terrorism".
"We do not know whether a real change has occurred in the situation. We hope so," Mr Sharon said.
Mr Abbas is trying to clinch a deal that would give him a stronger mandate in future negotiations with Israel.
On Friday some 3,000 Palestinian policemen were deployed in northern Gaza in an effort to halt rocket attacks on Israelis.