Bush has pulled back from an aim he set a year ago to establish a Palestinian state by the end of his second term, but Abbas told journalists in an interview on Friday that an independent state was "realistic, if we work on it from now".
Abbas said he did not believe Bush had intended to make his comments after their talks at the White House on Thursday.
"I had the impression that the comments of President Bush were not planned, that he had not set out to say what he did. We had no discussion about this topic," the Palestinian Authority president said.
"It was not a political position but a position expressed on the spot."
Bush surprised observers with his comment at a press conference after the White House talks.
"I had the impression that the comments of President Bush were not planned, that he had not set out to say what he did. We had no discussion about this topic"
"I believe that two democratic states living side by side in peace is possible. I can't tell you when it's going to happen. It's happening," Bush said.
"If it happens before I get out of office, I'll be there to witness the ceremony. And if doesn't, we will work hard to lay that foundation so that the process becomes irreversible," the US president added.
The road map to Middle East peace drawn up by the United States, Russia, the European Union and the United Nations originally foresaw a Palestinian state by the end of 2004.
But the moves have come to a halt and in 2004 Bush put back his deadline to the end of his second term, which is 2008.
Abbas said a Palestinian state should not take years to complete.
"I think if we start to work seriously, we will only need a few years or a year. It is important for us and the Israelis if they want a real peace," he said.
Abbas said there had to be an alternative negotiation channel between Israelis and Palestinians, similar to the secret talks that led to the Oslo peace accords and Palestinian autonomy in 1993.
"I proposed to the Americans the idea of a back channel for negotiations and I hope that they, and the Israelis, are going to accept it," he said.
"I am totally convinced that if we work seriously with the Israelis nothing will stop the creation of a Palestinian state [before 2009]," said the Palestinian leader.