The two leaders, both faced with skepticism at home over their handling of the Iraq war, are to meet on Tuesday afternoon for their first talks since Blair emerged from elections a month ago with a third term but weakened politically.
Bush and Blair will also discuss debt relief for Africa, in addition to efforts to train Iraqi troops, attempts to contain Iran's nuclear programme and the prospects for Middle East peace.
On debt relief, Blair expressed optimism. "We are a significant way towards a deal. I'm increasingly hopeful we will get it," he told reporters.
Blair came looking for support for his initiative to boost financial aid for Africa at a Group of Eight summit he is to stage in Gleneagles, Scotland, next month.
But Blair said there was no chance of Bush supporting Britain's "International Finance Facility", which would double aid for poor countries by issuing bonds against the future aid budgets of rich nations.
Blair is keen to increase aid to
Africa for tackling poverty
"There are certain things we know they are not going to do, that we are not asking them to do," Blair said in an interview with the Financial Times.
"We are not asking them to sign up to the IFF ... They are not going to do that and they've made that clear right from the very beginning."
A Blair spokesman said before the visit began that the two leaders did agree on other ways to tackle Africa's problems.
In what appeared to be a gesture to a close ally, White House spokesman Scott McClellan said the two leaders would announce a joint British-US initiative aimed at feeding the hungry in Ethiopia, Eritrea and other African nations threatened by famine.
The US contribution would include $674 million - enough to feed 14 million people - and a significant commitment will also be made by the British, McClellan said.
"We welcome what the administration has done but there is a lot more that needs to be done," said Blair, who vowed to press on.
Britain's finance facility plan envisions raising $25 billion to $50 billion a year by selling bonds on global capital markets.
Bush made clear his position last week, saying the proposal
"doesn't fit our budgetary process".
An official of the Oxfam charity criticised the Washington announcement as inadequate and said Africa doesn't need "yet more warm words followed by empty gestures".
Blair has staked his reputation on helping Africa during Britain's presidency of the G8 group of rich nations.
Bush and Blair were allies on the Iraq war and came under criticism at home for basing the decision to go to war on alleged weapons of mass destruction that were never found.
Blair has also pledged to address climate change at the Gleneagles summit, despite the US refusal to abide by the Kyoto treaty aimed at cutting greenhouses gases thought to contribute to global warming.