While appealing to both sides of the conflict on a day Palestinians set aside to mourn Israel's creation, Abbas expressed concern that the economic crisis in the Palestinian territories would deepen if not resolved soon.
"We expect the new Israeli government to enter into talks with us, as we are its partner and believe in a peaceful resolution," the ITAR-Tass and RIA-Novosti news agencies quoted Abbas as saying during a meeting with President Vladimir Putin.
In a separate speech broadcast on Palestinian radio and television, Abbas told Israel "we want to make a just and lasting peace with you."
"Let's sit at the negotiating table, away from the dictates and the unilateral policies, and let's stop the pretext that there's no Palestinian partner," he added. "The partner exists, and we extend our hand to you to make peace."
Abbas also signaled to the rival Hamas party that it, too, must pursue the path of diplomacy.
"ThePLO, which led our people in its most difficult times, would not have survived until now, or received international recognition, had it not been forthcoming in formulating courageous political initiatives," he said.
He also called on Palestinian militants in Gaza to halt rocket attacks on Israel that have prompted harsh reprisals.
"The futile 'missiles' fired from Gaza should be stopped, as they only justify Israel's aggression against our people," he said.
Israeli Foreign Ministry spokesman Mark Regev said his government wanted peace, but he dismissed the notion of bypassing Hamas and negotiating with Abbas.
"No one can ignore the reality following the Palestinian election; substantive political power has moved to Hamas," Regev said.
Israeli Prime Minister Ehud Olmert hopes to win international support for his plans to withdraw from much of the West Bank and will be presenting the program to U.S. officials in Washington next week.
Olmert is expected to meet with Abbas after the Washington trip, though formal peace talks appear unlikely. Olmert says he would prefer a negotiated accord but will act unilaterally if Hamas does not soften its line within months.
Abbas said he had come to Russia — a member of the so-called "Quartet" of international Mideast peace makers — to discuss ways to move the political process forward.
"The only way is talks that would lead to a resolution on the conflict between the Palestinians and the Israelis, and at which a solution would be found that satisfies both sides and puts an end to unresolved problems," he said, according to the news agencies.
The meeting took place at Putin's residence in the Black Sea resort of Sochi.
Putin, who has sought to boost Russia's Mideast role, called Russia "a friend of the Palestinian people" in televised comments and praised Abbas for "big efforts to normalize the atmosphere in the Palestinian territories."
Abbas thanked Putin for transferring $10 million to an account controlled by Abbas earlier this month, calling Russia a "friendly state that invariably supports the Palestinian people."
The decision to send the aid came before the Quartet — which also includes the United States, the European Union and the United Nations — decided last week to set up a temporary trust fund to funnel aid directly to the Palestinian people, bypassing the Hamas government.
At a meeting of EU foreign ministers in Brussels, Belgium, External Relations Commissioner Benita Ferrero-Waldner said she hoped the fund would be operating by June.
The West cut off hundreds of millions of dollars in annual aid after Hamas was elected to power earlier this year. Israel also stopped transferring hundreds of millions of dollars in tax and customs revenues it collects on behalf of the Palestinians.
As a result, salaries for 165,000 Palestinian government workers are two months late. The Palestinians need $116 million a month to pay salaries.
Israel now has agreed to release an unspecified amount of humanitarian aid.
Putin invited Hamas leaders to Moscow for a March meeting that provoked anger in Israel and surprise among the other Quartet members. But Russia has made no apparent headway in persuading Hamas to renounce violence and recognize Israel.
Olmert's plan to dismantle dozens of isolated Jewish settlements while strengthening settlement blocs would involve a significant pullback. But it still falls short of the Palestinian claim to all the West Bank and east Jerusalem — territories Israel captured in 1967 along with the recently evacuated Gaza Strip.
Olmert believes the pullback is needed to ensure Israel's status as a democracy with a Jewish majority.
Abbas' broadcast speech marked "the Naqba," or "catastrophe" — the term Palestinians use to describe Israel's creation on May 15, 1948. Some 700,000 Palestinians fled or were driven from their homes during the war that followed the declaration of the Jewish state.
About 2,000 Palestinians from rival factions joined a commemoration outside the parliament building in Gaza City, waving banners, Palestinian flags and models of keys symbolizing lost homes in what is now Israel. Ambulance sirens wailed for one minute to mark the occasion.
"Refugees are the cause of the conflict, and their return is the solution," a large billboard said.
In previous years, Naqba crowds numbered hundreds of thousands. The low turnout this year appeared to be related to economic hardship in Palestinian territories, which has made travel difficult, and to rivalry between Hamas and Abbas' Fatah.
Hamas planned its own event later in the day in the southern Gaza town of Rafah.