"I was pleased to note that the United Nation's Security Council passed a resolution which confirms that the bilateral negotiation process is irreversible and it is a path to a Palestinian state and a path to peace in the Middle East," he added.
'No turning back'
Abbas praised the outgoing US president's role in the peace process saying: "There is no doubt that we will continue these efforts and the peace negotiations, but everything will be based on the foundation, and that foundation was laid by you during your time in office."
Saeb Erekat, chief Palestinian negotiator, warned in an interview with Al Jazeera that the US could not "defeat extremism with guns and marines" and that they should "ask the Palestinians what's needed".
However, Erekat also said that Bush's comments meant that "no-one can reverse the idea of a two-state solution".
When asked if Bush would put pressure on Israel to ease its blockade of Hamas-controlled Gaza, Erekat said the US president understood the situation but did not commit to negotiating an end to the siege.
Earlier this week, the quartet of Middle East peace negotiators - the European Union, America, Russia and the United Nations - said there was no turning back from US-led talks between Israel and the Palestinians, despite failing to produce a peace deal by the end of 2008.
The quartet said peace negotiations launched in November last year in Annapolis, Maryland should be accelerated.