In a speech to mark Nakba, a day of mourning for Palestinians recalling the day Israel was founded in 1948, Mr Abbas said Hamas, the Islamic movement that heads the Palestinian government, should honour existing peace agreements.
Palestinians should not be satisfied with "fiery speeches and slogans that could bring about international isolation", Mr Abbas said, repeating his longstanding call for Hamas to renounce violence.
Appealing to Israel, where Mr Abbas is widely seen as a weak leader unable to engage in peacemaking while Hamas is in power, he said: "We want to make a just and permanent peace with you.
"Let's make this year the year of peace, let's sit at the negotiations table away from the policy of diktats and unilateralism. Stop making excuses there's no Palestinian partner, the partner is there," Mr Abbas, now on a visit to Russia, said in an address.
Hamas defeated Mr Abbas's Fatah movement in January polls and took office in March. It is sworn to Israel's destruction and has ruled out peace talks.
Hamas stands firm
In a speech in a soccer stadium in the southern Gaza town of Rafah, Prime Minister Ismail Haniyeh rejected any change in Hamas's stance towards Israel.
"As I entered this stadium, a woman gave me this necklace, telling me: 'please do not make concessions', and I tell her and I tell all woman and men of our people: I swear to God we will not make concessions," Mr Haniyeh said.
Meanwhile Israeli soldiers killed two Palestinian militants during a raid in the occupied West Bank on, Palestinian security sources and medics said.
They said the two gunmen were killed during an exchange of gunfire with Israeli troops in the West Bank city of Nablus.
A third gunmen was injured in the clash and was arrested by Israeli forces, the sources said.
An Israeli military source said soldiers had hit three gunmen inside a building in the city said to be housing a wanted militant.
Medics at the hospital said they had found a green wristband written in Arabic on each of the two dead men identifying them as being with the militant group Islamic Jihad.
Earlier, an Israeli air strike on a car in the nearby town of Khan Younis wounded three Islamic Jihad militants. The Israeli military said they were "en route to carrying out an attack against Israel".
Mr Abbas made his peace offer a week before Israeli Prime Minister Ehud Olmert visits the White House to outline his plan to remove isolated Jewish settlements in the occupied West Bank, bolster major enclaves and draw a permanent frontier.
Mr Olmert and US President George W Bush are also expected to discuss Iran's nuclear program.
Announcing the May 23 visit, the White House said the talks would focus on "the strong bilateral relationship between the United States and Israel as well as a wide range of regional and international issues".
In his speech, Mr Abbas warned Israel unilaterally setting "final borders", as Mr Olmert has pledged to do by 2010 if peace talks cannot be resumed, would increase violence and extremism.
He urged Israel to release the US$55 million (A$71.4 million) in monthly tax revenues it has withheld from the Palestinians since March.
Nakba marked
Crowds gathered in the centre of Ramallah to hear Mr Abbas's speech over loudspeakers after standing in silence as sirens wailed to mark Nakba 58 years ago.
Arab states attacked Israel the day after it was proclaimed on May 14, 1948. In the war, about 700,000 Palestinian Arabs fled or were driven from their homes in what is now Israel.
Hamas now not only has virtually no income but has inherited government coffers it says were US$1.3 billion (A$1.7 billion) in debt. Hospitals are short of medicine and 165,000 government employees have not been paid.
The EU says it hopes to get a new mechanism for channelling aid to the Palestinians, bypassing Hamas, up and running soon.