Blair, is meeting Bush in Washington on Friday for talks set to be dominated by the current violence in Iraq, insisted there were no strategic differences with Bush as he arrived in the United States.
"The common aim and purpose is what is crucial," Blair told reporters after meeting United Nations Secretary General Kofi Annan in New York on Thursday.
However the British premier faced a series of calls to use Britain's status as the closest ally of the United States in Iraq to exert more leverage on what was happening in the country.
Blair is also expected to address Bush's controversial decision this week to change US policy towards the settlement of the Israeli-Palestinian conflict.
Blair's former foreign minister said on Friday that the prime minister should use the summit to pressure Bush to end the tough military campaign by US forces against resistance fighters in Iraq.
Cook left the government
in protest over the war on Iraq
Writing in the Independent newspaper, Robin Cook - who quit Blair's government in protest over the Iraq war - said Bush was wrong to think he could make progress in Iraq by military means "regardless of political cost".
"The most important job for Tony Blair today is to convince the Bush administration that they are not engaged in a military operation to beat a discrete enemy, but in a political exercise to win the hearts and minds of a whole people," said Cook, who was foreign secretary from 1997 to 2001.
But even though the White House huddle would be "the most
crucial diplomatic meeting of Tony Blair's career", Cook doubted the prime minister would confront the president head-on.
"Spelling out bluntly to someone as powerful as the president of the United States that he has got it wrong is not Tony Blair's natural suit," he wrote.
Speaking on BBC radio on Friday, opposition Conservative leader Michael Howard said Blair was right to press an enhanced UN role in Iraq, but expressed concern about the nature of the British presence in Baghdad.
Britain shares the military burden
but wields little political influence
London's first chief envoy to post-war Baghdad was former UN ambassador Sir Jeremy Greenstock. But eyebrows were raised when he was replaced at the end of March by a comparatively junior diplomat, David Richmond.
Howard said the British representative ought to be a genuine deputy to top US administrator Paul Bremer "so that he is fully plugged-in to the process, has a full say in the decisions that are taken".
Liberal Democrat leader Charles Kennedy, whose party opposed the Iraq war, said Blair must warn Bush of the "massive degree" of international disquiet about the "tactics and the methodology" employed by US forces in Iraq.
Blair may also seek clarification of Bush's decision this week to change US policy towards the issue of Palestine.
Bush declared on Thursday that the Palestinians could not realistically hope for a return to pre-1967 borders, nor argue for a right of return for refugees from Israel.
European leaders and the UN have expressed concern that the White House is unilaterally disregarding international law - which favours the Palestinians' demands - and undermining the prospect of a negotiated settlement in order to back its Israeli ally.
Bush's move to back Israeli Premier Ariel Sharon's plan for a partial withdrawal from occupied Palestinian territory while holding on to larger illegal settlements in the West Bank has also angered Arab and many Muslim governements.