Rupert Murdoch joined in an "over-crude" attempt by US Republicans to force Tony Blair to accelerate British involvement in the Iraq war a week before a crucial House of Commons vote in 2003, according to the final volumes of Alastair Campbell's government diaries.

In another blow to the media mogul, who told the Leveson inquiry that he had never tried to influence any prime minister, Campbell's diary says Murdoch warned Blair in a phone call of the dangers of a delay in Iraq. The disclosure by Campbell, whose diaries are serialised in the Guardian, will pile the pressure on Murdoch in light of his evidence to the Leveson inquiry.

The Cabinet Office released information on Friday that raised doubts about Murdoch's claim that Gordon Brown pledged to "declare war" on News Corporation after the Sun abandoned its support for Labour in September 2009. It supported Brown's claim that he never made such a threat by saying that the only phone call between the two men during the period took place on 10 November 2009 and focused on Afghanistan.

Murdoch tweeted in response: "I stand by every word is aid [sic] at Leveson." But there will be fresh questions about one of Murdoch's most memorable declarations from his appearance before the inquiry in April. The founder of News Corporation said: "I've never asked a prime minister for anything."

Campbell wrote that on 11 March 2003, a week before the Commons vote in which MPs voted to deploy British troops to Iraq, Murdoch intervened to try to persuade Blair to move more quickly towards war. "[Tony Blair] took a call from Murdoch who was pressing on timings, saying how News International would support us, etc," Campbell wrote. "Both TB and I felt it was prompted by Washington, and another example of their over-crude diplomacy. Murdoch was pushing all the Republican buttons, how the longer we waited the harder it got." The following day, 12 March, he wrote: "TB felt the Murdoch call was odd, not very clever."

Campbell's description of Murdoch's intervention is one of a series of disclosures in his diaries, The Burden of Power, Countdown to Iraq, which are serialised in the Guardian on Saturday and Monday. The diaries show:

• Blair believed that the Prince of Wales had been "captured by a few very rightwing people", according to Campbell, after the Daily Mail published leaked letters from the prince about a US-style compensation culture in 2002. Blair "liked, rated and respected" the Queen but thought her heir tried to have a "dig" at the Labour government in a speech during her golden jubilee in 2002.

• Gordon Brown agitated so aggressively against Tony Blair – demanding a departure date soon after the 9/11 attacks – that Downing Street concluded in 2002 that the then chancellor was "hell-bent on TB's destruction".

The diaries will raise questions about Brown's claim at Leveson that he and his staff never briefed against Blair. Campbell provides specific examples of when Brown and his chief aide, Ed Balls, were suspected of doing just that. In one example, the former health secretary Alan Milburn told Blair that Brown encouraged MPs to defy a government three-line whip to vote against foundation hospitals in 2003.

• Blair was "thwarted" from joining the euro by Brown and Balls in 2003. On 11 June 2003, two days after Brown concluded that Britain had not yet met his five tests on euro membership, Campbell wrote: "Things just hadn't worked on the euro and TB was pretty fed up...The judgment was settling that GB had basically thwarted him. TB feared we were making the wrong decision for the wrong reasons."

Campbell said he had mixed views about Brown. He told the Guardian: "I do have very conflicted views about Gordon. On the one hand he could be extraordinarily difficult to deal with. But on the other hand he could be absolutely brilliant. Often we were sitting there longing for the brilliant to be in charge and for the impossible to fade away and it never quite happened. During this period it is the first time that Tony does at least articulate the possibility of actually sacking him. And at various points [he] says I am going to do it. Of course he never did. I completely understand why he decided to stick with Gordon because, as Tony keeps saying throughout the diaries: 'Look, when it comes to ability, he and I are head and shoulders above the rest.' That may sound a bit arrogant but most people will accept that."

Campbell's disclosure of Murdoch's intervention on the eve of the Iraq war is the second substantive example to raise questions over the News Corp chairman's claim that he never tried to influence any prime minister. John Major told Leveson on Tuesday that Murdoch told him in February 1997, three months before the general election, that he would withdraw support for the Tories unless the then prime minister changed his policies on Europe.

Major told the inquiry: "If we couldn't change our European policies, his papers could not and would not support the Conservative government."

Campbell told the Guardian that Murdoch's intervention on Iraq was a "very rightwing voice" that came "out of the blue" adding: "On one level [Murdoch] was trying to be supportive, saying I know this is a very difficult place, my papers are going to support you on this. Fine.

"But I think Tony did feel that there was something a bit crude about it. It was another very rightwing voice saying to him: look isn't it about time you got on with this? I think, as I recall Tony saying, he didn't think it was terribly clever."

Campbell also mentioned the Murdoch phone calls in a second witness statement to the Leveson inquiry last month. News Corp believes there was nothing improper about the phone call, one of three, because the support of the Sun and News of the World for the war was well known.

Lord Justice Leveson, whose lead counsel, Robert Jay, asked Murdoch about the calls, also indicated that it was "reasonable" for him to have views on such international matters.

Leveson told Murdoch: "You've mentioned that you talked about Afghanistan, and it would be perfectly reasonable for you to have a view on that. Lots of people will. And your view may be informed by your worldwide contacts through the businesses that you operate. That's merely your view."

Murdoch addressed the phone calls in his witness statement to the Leveson inquiry. He said: "As for the three telephone calls with the then prime minister, Tony Blair, in 2003, I cannot recall what I discussed with him now, nine years later, or indeed even if I spoke with him at all. I understand that published reports indicate that calls were placed by him to me. What I am sure about is that I would not in any telephone call have conveyed a secret message of support for the war; the NI titles' position on Iraq was a matter of public record before 11 March 2003."

He then cited four articles from the Sun and the News of the World which illustrated their "pro-war stance" before 11 March 2003 when the main phone call took place.

In his testimony to the inquiry said he did not remember the calls but added that the Sun's support for the Iraq war was well known. "I don't remember the calls. The [call on] 11th might even have been calling me for my birthday, but no, our position on the war had been declared very strongly in all our newspapers and the Sun well before that date."

The company said tonight: "It is complete rubbish to suggest that Rupert Murdoch lobbied Mr Blair over the Iraq war on behalf of the US Republicans. Furthermore, there isn't even any evidence in Alastair Campbell's diaries to support such a ridiculous claim."