The communications between the leaders are seen as key pieces of evidence in the inquiry into British involvement in the US-led invasion of Iraq.
The inquiry, which began in 2009 and is led by Sir John Chilcot, has been delayed because the exchanges have yet to be released by the British government.
The spokesman for the Cabinet Office said the communications were a “particularly privileged channel of communication.”
“The Government is currently engaged in discussions with the inquiry. All sides recognize that this raises difficult issues involving legal and international relations considerations,” the spokesman said. “Any suggestion that the US has a veto is wrong.”
Sir John has written to British Prime Minister David Cameron asking for access to 25 notes from Blair to Bush. He has also asked for 130 records of phone conversations between Blair and Bush, and Gordon Brown and Bush.
But according to senior diplomatic sources in the US and Whitehall who spoke to the Independent , officials in the White House and the US State Department have refused to declassify the pre- and post-war communications between George W. Bush and Tony Blair.
Media reports suggest the Bush-Blair exchanges are likely to provide critical evidence of the covert way that Tony Blair committed 45,000 British soldiers to the US-led invasion.