The inquiry into Britain’s involvement in the Iraq war could publish its long-awaited conclusions in 2014 after discussions between Tony Blair and George W Bush are published, news reports say.

A government source told the Independent newspaper that “good progress” had been made in talks between the inquiry body and the government on declassifying many of the records of their conversations.

There had been fears that Blair – who as prime minister committed British forces to the US-led invasion of Iraq in 2003 after forming a close bond with then-president Bush – and the US administration would block the release of the confidential papers.

But the Independent and the Guardian both reported that a compromise had been reached that should allow the documents to be published in the next few months, with as little redaction as possible.

“There are likely to be some redactions – but only where absolutely necessary,” the government source told the Independent.

The release of the documents would allow the Iraq Inquiry to complete its final task of contacting people who are set to face criticism in the report and allow them to defend themselves.

The issue of the records of discussions between Blair and Bush has been one of the major obstacles to the progress of the inquiry, which was set up in 2009.

A letter to the government from the inquiry’s chairman, former senior civil servant John Chilcot, in November said he had asked for the disclosure of 25 written notes from Blair to Bush and more than 130 records of conversations between Bush and either Blair or his successor Gordon Brown.

The Guardian reported that Blair was “relaxed” about the publication of his correspondence with Bush.

Britain was the second largest contributor of troops to the invasion after the US.

A total of 179 military personnel were killed in Britain’s six-year involvement in Iraq.