Shadow Foreign Secretary William Hague has said a Tory visit to Washington will "pave the way" for a meeting between David Cameron and George Bush.
William Hague is meeting Bush aide Karl Rove
Mr Hague is due to meet key Bush aide Karl Rove later on Thursday.
In 2004, Mr Rove reportedly told ex-Tory leader Michael Howard: "You can forget about meeting the president full stop. Don't bother coming."
The White House was reportedly angry about Mr Howard's call for Tony Blair to quit over the Iraq war.
Ahead of the trip, the Conservatives insisted any disagreements with Mr Bush's Republican party over Iraq were "in the past".
But Mr Hague, who is in Washington with shadow defence secretary Liam Fox and shadow chancellor George Osborne, said he would be raising concerns about the war and other issues.
"Mistakes have been made on Iraq. We still believe it was the right thing to do but that in the handling of Iraq over the last couple of years, many mistakes have been made," he told the BBC Radio 4 Today programme.
"I think we can do that in a very civilised way. These points do need to be made to American policymakers."
Mr Hague said he hoped the Tory delegation's visit would lay the ground for Mr Cameron to meet Mr Bush.
He said he "did not have a timetable" but he was "sure" such a meeting would take place "later in the year", although a Conservative spokesman later indicated it may take longer than that to set up.
Mr Hague has requested a private meeting with US Secretary of State Condoleezza Rice but this has not yet been confirmed.
But all three members of the delegation will meet Republican senator John McCain, a possible candidate for the 2008 presidential race.
They will also hold talks with senators from both the Republican and Democrat side, including Republican majority leader Bill Frist.
In a keynote speech later on Thursday, Dr Fox will urge Mr Bush not to scale back his commitment to the Anglo-American Joint Strike Fighter programme.
The trip comes as the Tories study the impact of the internet on American politics.
Tim Montgomerie, a former aide to Iain Duncan Smith who is now editor of the Conservative Home website, has just returned from Washington.
"I'm convinced blogging and other web platforms are going to be increasingly important in Britain too," he said.
Mr Montgomerie has been looking at how some US conservative internet campaigners attacked Democrat contender John Kerry's war record. He will send a report on his findings to Tory chairman Francis Maude.
Some reports had suggested Mr Montgomerie could be used in the UK to tackle perceived left-wing bias in the BBC and other media outlets.