The British prime minister arrived in Washington late on Thursday and dined with the president - the first world leader to congratulate Bush in person on his re-election.
Their joint press conference on Friday will give Bush an opportunity to speak at length in public about his plans for Middle East diplomacy after the death of the veteran Palestinian leader in France.
"I think we've got a chance," Bush said several hours before the 75-year-old Arafat was declared dead. Afterwards, the US president called it "a significant moment" for the Palestinians in their quest for peace and an independent state.
Blair is keen to win a fresh commitment from Bush for a more active US role in mediating the Palestinian-Israeli conflict, after years in which Israel and the United States refused to deal with Arafat.
So far US officials have been cautious about raising expectations as long as it is not yet known who will replace the veteran Palestinian leader.
"I think we've got a chance"
US President George Bush
"It really depends on what comes out of this and who's running the show," said one official who asked not to be named.
Blair's officials have said they do not expect a concrete announcement of a new timetable for Middle East diplomacy to emerge from the talks.
But Blair's spokesman also said the prime minister expected to deliver a clear "signal of intent to help drive the process forward".
There have been no serious peace negotiations since the collapse of former US president Bill Clinton's efforts to broker a deal at Camp David in 2000.
The second Palestinian intifada or uprising against Israel began soon after.
Bush was the first US president to officially call for a Palestinian state.
With the road map peace plan - backed by the United States, the EU, Russia and the United Nations - all but dead, US officials have pinned their hopes on Israeli Prime Minister Ariel Sharon's plan to withdraw from all settlements in Gaza and four in the West Bank.