Hamas was among the leading Palestinian resistance groups on Sunday which denied the Israeli account that they had agreed to a ceasefire, while saying they could accept a period of calm if Israel halted all attacks first.
Mofaz had told Israel Radio that Hamas and Islamic Jihad, the most prominent Palestinian resistance groups, had agreed to the ceasefire in return for a future role in the Palestinian Authority.
"This agreement was sealed in exchange for the future integration, notably of Hamas, in the Palestinian political institutions," Mofaz said in a reference to the Palestinian Authority.
"The agreement constitutes a positive sign and a success for Abu Mazin. We are pleased with it but must closely follow the way the terrorist organisations conduct themselves on the ground."
Truce on condition
Speaking to Aljazeera from Gaza, Sami Abu Zuhri, spokesman for Hamas movement, said: "Mofaz's announcement is incorrect. We have not discussed a month-long truce. We have only said the movement is willing to discuss seriously a truce in case Israel halts its aggression against the Palestinian people."
Israel is accused of making
Abu Zuhri said: "There is no truce without clear and guaranteed Israeli commitments," adding that "Israel is known for empty announcements.
"We want international guarantees that secure an end to all kinds of Israeli aggression against our people."
Responding to Mofaz's statement that a month-long ceasefire deal had been reached on the condition that Hamas would get a future role in Palestinian political and official institutions, he said: "This matter is an internal Palestinian issue and Mofaz has nothing to do with it.
Abu Zuhri continued: "We have discussed Hamas' integration into Palestinian political establishments in order to organise the Palestinian community based on political partnership, reforms and other internal issues.
"These matters are still being discussed and we may make announcements later."
"There is no truce without clear and guaranteed Israeli commitments"
Sami Abu Zuhri,
He added: "I believe there is a Palestinian national agreement on all these points and on all Hamas suggestions."
There was no immediate comment from Abbas or the Palestinian Authority.
Abbas met with Hamas leaders late on Saturday. His office put out a statement after the meeting, saying the talks had been positive and centred on "the return of calm that is in the national interest of Palestinians".
But neither side mentioned any truce.
Ready for truce?
On Saturday three Palestinian groups, including al-Aqsa Martyrs Brigades linked to the mainstream Fatah, said they were ready to back the new Palestinian leader's bid to end armed conflict with Israel.
The al-Aqsa Martyrs Brigades
called on Israel to cease attacks
The Brigades said its member groups were prepared to halt attacks through a mutual ceasefire - a welcome boost for Abbas who is seeking to persuade Israel of his ability to impose order in the territories.
Among the Brigades' conditions for any agreement to a ceasefire were that Israel announce a cessation of its military operations, halt its policy of targeted assassination of militants, and release Palestinian prisoners.
Body handed over
In a separate development, the Israeli army handed over the body of a Palestinian killed while trying to infiltrate Israel's West Bank separation barrier wall on Saturday, Palestinian security sources said on Sunday.
Salah al-Din Huli, 19, was killed near the northern West Bank town of Qalqilya, the sources said.
An Israeli army source said troops had fired warning shots before killing the teenager when he pressed ahead with the illegal crossing.
The latest death brings to 4715 the overall toll since the September 2000 start of al-Aqsa Intifada, including 3660 Palestinians and 981 Israelis.