The Palestinian president was speaking at a news conference with Angela Merkel, the German chancellor, in Ram Allah on Monday.
"Nothing will prevent me from serving the three years left of my time as head of the authority," he said. "I intend to continue implementing my political programme during this period."
Despite the victory of Hamas, which does not recognise Israel's right to exist, the Palestinians remain committed to the peace process with Israel, Abbas said he told Merkel.
"We reiterated our commitment to the peace process through negotiations and according to international legitimacy," he said.
"Our main goal as Palestinian people is to reach an independent state with Jerusalem as its capital to live in peace beside Israel."
Abbas was elected president in succession to the late Yasser Arafat in January 2005.
But the heavy defeat of his long-ruling Fatah faction to Hamas in last week's Palestinian parliamentary election had raised doubts about his ability and appetite to continue in the post.
Poverty is an ongoing problem
for many Palestinians
Abbas also said he planned to meet leaders from Hamas in the next two weeks to discuss forming a new government.
"I will definitely meet the Hamas leadership to form the coming government, and I hope this will not be more than two more weeks," he said.
Abbas went on to urge the international community to maintain its financial aid to the Palestinians.
Commenting on his discussions with Merkel, he said: "Our talks focused on the need to continue this aid so that our people can stand on their own feet."
Abbas was speaking as key world powers sought to thrash out a strategy towards Hamas with some Europeans and the US warning the group to renounce violence or face aid cuts.
At a meeting in Brussels on Monday, the European Union urged Hamas to renounce violence and recognise Israel as key conditions for continuing to give aid to the Palestinian Authority.
Merkel insisted Berlin would not fund a Hamas-led Palestinian Authority unless the group accepted those terms as well as previous agreements between the Israelis and Palestinians.
"Germany will not support a Palestinian Authority that does not recognise Israel," she said.
"We expect all political forces that assume responsibilities ... to firstly recognise Israel's right to exist, secondly not resort to violence ... and thirdly accept committed steps in the peace process and continue this process."
US and European diplomats are secretly and publicly meeting Hamas leaders in the West Bank, Palestinian sources close to Hamas have told Aljazeera.net.
The sources said at least five meetings between Western diplomats and Hamas leaders took place in the past few days.
On Saturday, three former senior US ambassadors to Middle Eastern countries met a number of elected Hamas leaders in the West Bank, including Shaikh Nayef Rajoub.
Rajoub reportedly spoke at length with the former diplomats, telling them that Hamas would succeed in governance and peace-making as it did in resisting the Israeli occupation.
"We reiterated our commitment to the peace process"
"We will not beg to meet Western diplomats, but if they come to visit us, we will receive them with all due respect," he told Aljazeera.net.
For their part, EU diplomats, representing their respective governments, reportedly were planning to meet the Hamas leadership either directly or through a third party.
One European diplomat said that the EU was holding only "exploratory meetings" with Hamas.
"We would like to know to which extent Hamas is prepared to negotiate peace with Israel and indeed recognise Israel's existence," said the diplomat, who asked for anonymity because he was not authorised to speak to the media.
Aljazeera.net's Khalid Amayreh in the West Bank contributed to this report