Sir John Chilcot and Cabinet Office agree the 'gist' of the exchanges can be made public, but not the full correspondence

The Chilcot inquiry into the Iraq war has been accused of allowing a whitewash after it struck a deal with ministers to publish the gist of letters between Tony Blair and George Bush but not the full correspondence.

The publication of the Chilcot report has been overdue for several years with discussions in recent months focused on 25 notes from Blair to Bush and 130 records of conversations.

After intense negotiations, Sir John Chilcot, who has been leading the inquiry since 2009, has now agreed with the Cabinet Office that the gist of the conversation can be made public, but direct quotation from the notes will be kept to "a minimum necessary for the inquiry to articulate its conclusions". He has also agreed that use of material from the letters "should not reflect President Bush's views".

No decision has been taken, however, on exactly which quotations from the Bush-Blair correspondence will be published or how the gist will be phrased. There is also now an agreement to release a small number of extracts from the most "critical" minutes of more than 200 cabinet-level discussions.

Chilcot was told by former cabinet secretary Sir Gus O'Donnell in 2011 that there was no way the notes or records of correspondence between Bush and Blair could be published in their entirety, even with redactions.

The deal means the report may now be published by the end of the year after senior politicians, including David Cameron and Nick Clegg, demanded a speedier resolution. Blair this week repeated denials that he was responsible for the blockage and Whitehall sources said the main source of objections was the US.

However, on Thursday, a number of politicians raised concerns that the Chilcot inquiry had capitulated to the demands of the Cabinet Office by agreeing not to publish the full correspondence. John McDonnell, Labour MP for Hayes and Harlington, said the failure to publish the entire dialogue "confirms suspicions of whitewash" and undermines the credibility of the whole report.

The level of disclosure was also criticised by Paul Flynn, Labour MP for Newport West, who said it was crucial the public was not simply given the partial truth about the decision to go to war in Iraq. "It's a shame it has been going on for so long and they are still unwilling to tell us the whole truth," he said.

Andrew MacKinlay, former Labour MP for Thurrock, who sat on the Commons foreign affairs committee, said he thought Chilcot had surrendered in a "bad, bad day for democracy and justice". "The establishment of this country, and the security and intelligence services have won again. Truth has lost out," he said.

The development emerged through a letter published on the inquiry's website, in which Chilcot wrote to the government to "record his pleasure" that agreement had been reached on an issue that had "raised difficult issues of long-standing principle".

The inquiry's website said: "Detailed consideration of gists and quotes requested by the inquiry from communications between the UK prime minister and the president of the United States has now begun. It is not yet clear how long that will take, but the inquiry and the government should work to complete the task as soon as possible."

The letter also revealed that some "potential gaps" in material had been identified which had now been addressed, "including some material received by the inquiry very recently".

Pressure has been mounting for the report into the Iraq war to be published as soon as possible. Earlier this month, Cameron said he wanted the report by the end of the year, adding: "I think we shouldn't have to wait much longer."

The Scottish National party wants the report published before the referendum in September, while Labour insiders are nervous about its conclusions coming out too close to next May's general election.

Clegg, who oversees the Cabinet Office, appeared to suggest last month that some of those in line for scrutiny were to blame for holding up the process, which began in 2009 and has cost millions of pounds.

"I'm sure Chilcot himself would like to get on with it as quickly as possible," Clegg said. "I can't comment on exactly the reasons why, given there's a lot of to-ing and fro-ing about what is finally produced in published form in the report.

"This involved a lot of people, a lot of legalities and, of course, is a very, very sensitive issue.

"But I really do think everybody involved, including those who know they will be subject to renewed scrutiny from the Chilcot report, all now accept that it is time that the report was published so the record can be scrutinised in the most objective way possible."

He said those who might not like being subject to scrutiny must accept that it would happen, given that it was "one of the most momentous, one of the most catastrophic decisions in British foreign policy. I would say the most catastrophic decision since Suez".

The inquiry and the Cabinet Office will now have to agree exactly what will be published from the Bush-Blair records. After that, the process of Maxwellisation will begin, in which the inquiry puts its conclusions to those criticised.

A spokesman for the Cabinet Office said the government is "pleased that agreement on a way forward on both cabinet papers and UK/US exchanges has now been reached with the inquiry".

"This allows for the declassification and publication of the material the inquiry believes it needs to explain its conclusions," he said. "Resolving this issue has taken longer than originally hoped but these are sensitive issues.

"The UK/US head of government channel is very important and must be handled sensitively. The government and the inquiry are working to ensure the inquiry's report is published as soon as possible and the government is doing everything it can to facilitate that."