Story Highlights• NEW: UK leader Tony Blair meets with Palestinian leader Mahmoud Abbas
• NEW: Blair says the international community should support Abbas
• Palestinian PM rejects Abbas' call for early elections
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RAMALLAH, West Bank (CNN) -- Palestinian leader Mahmoud Abbas and British Prime Minister Tony Blair met for talks Monday, with both leaders urging new efforts to resume the Mideast peace process.
Blair said the international community should support Abbas, whose Fatah faction is locked in a power struggle with the ruling party Hamas.
Abbas on Monday also repeated his call for early elections in the Palestinian territories -- a move that Hamas has rejected.
Hamas and Fatah have agreed to a cease-fire after street battles left at least two people dead, leaders of other parties involved in the talks announced early Monday.
Clashes between gunmen loyal to Fatah, led by Abbas, and Hamas, which controls the Palestinian government, escalated Sunday after Abbas called for the new elections.
Palestinian Prime Minister Ismail Haniya on Sunday rejected Abbas' call for early elections
The cease-fire took effect shortly after midnight Sunday, according to representatives of the Popular Front for the Liberation of Palestine and Democratic Action, two parties that helped negotiate the deal.(Watch streets of violence in Gaza )
The streets of Gaza City were quiet after the proclamation. There were sporadic reports of isolated incidents.
Officials from Hamas and Fatah confirmed their factions had signed onto the plan, but neither party sent officials to the news conference where the deal was announced.
According to the Popular Front and Democratic Action, both sides agreed to pull their gunmen off the streets, stop demonstrations and put an end to provocative statements in Palestinian news media.
Bowing to pressure from Egyptian officials, Fatah also agreed to release seven Hamas members arrested over the weekend, sources in Abbas' office said.
Fatah and Hamas fighters fought an intense gun battle near Abbas' office in Gaza one day after he delivered an impassioned speech calling for new elections. At least one person -- a 19-year-old female university student -- was killed, medical sources said. Abbas was in the West Bank and not in his Gaza office at the time.
Additionally, Hamas militants fired several mortar shells that hit near Abbas' compound, but there was no sign of casualties, said Wa'el Dahab, a spokesman for the Palestinian presidential guard.
Elsewhere, three Palestinians were wounded in Jabaliya when Hamas militants fired on a Fatah rally, Palestinian medical sources said.
Also in Jabalya, sources in Fatah's Al Aqsa Martyrs Brigades said that militants from Hamas' Izzedine al Qassam killed one of their field commanders and kidnapped one of their members.
And in a separate Jabaliya incident, Al Aqsa kidnapped two members of Izzedine al Qassam, the Al Aqsa sources said.
Earlier in the day, suspected Hamas gunmen attacked a training camp for the Palestinian presidential guard, killing one person, Palestinian security forces told CNN.
And suspected Fatah gunmen fired on a convoy carrying Foreign Minister Mahmoud Zahhar, but no one was wounded in the attacks, Palestinian security sources and Hamas sources said.
Fighting between Hamas and Fatah has spiked since Thursday, when Haniya was attacked as he tried to re-enter Gaza with millions of dollars he raised during a tour of neighboring countries.
Haniya and Hamas -- which the United States, Israel and the European Union consider a terrorist organization -- took over the Palestinian government from Fatah in last January's elections, leading to sanctions that have crippled the Palestinian economy.
Haniya said early elections would be unconstitutional and that Hamas would not participate, an adviser to the prime minister said.
Abbas said the elections would take place within three months.
But Saeb Erakat, chief Palestinian negotiator, told CNN that preliminary work needs to be done by the Palestinian election committee, after which the committee could recommend a time frame to Abbas.
Then he would issue a decree to carry out the elections.
Palestinian leader Mahmoud Abbas, right, welcomes British Prime Minister Tony Blair on Monday.
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