President Bush was helping John McCain to raise money for the coming presidential election yesterday, even as the Republican nominee did his best to hold at arm’s length the man he hopes to succeed in the White House.

They had not appeared in public together since March 5 and were scheduled to do so only fleetingly last night, with a planned photocall at Phoenix airport, in Mr McCain’s home state of Arizona, taking place long after evening television news bulletins had been broadcast.

Mr McCain has no plans to attend two other fundraisers featuring Mr Bush today in Utah. Last night’s event was being held behind closed doors, away from the media.

Hours before their awkward — and private — embrace in Phoenix, Mr McCain used a speech on nuclear proliferation to assert his independence from a President whose approval ratings are languishing below 30 per cent. Speaking in Denver, Colorado, he promised to reduce the US arsenal of missiles and scrap one of the Administration’s pet projects, the Robust Nuclear Earth Penetrator, or so-called bunker buster, saying that it was a “weapon that does not make strategic or political sense”.

He also expressed scepticism about the development of any new nuclear armoury that was not “absolutely essential for the viability of our deterrent”. Instead, Mr McCain set out a vision for a foreign policy that would build a community of nations and reject the unilateralism “of the United States acting alone”.

In recent weeks Mr McCain has criticised Mr Bush repeatedly on other subjects, such as climate change, where he said their differences are “longstanding, significant, deep and strong”, as well as saying that the White House should have stopped Washington’s “out-of-control” spending.

His speech in Denver, however, was interrupted three times by anti-war protesters, reflecting how tightly he remains bound to the President’s strategy in Iraq, even though he claims to be “sick at heart” about mistakes made at the outset of the action. “I will never surrender in Iraq,” he told the hecklers.

In an interview published yesterday, Mr McCain claimed that Barack Obama, his likely Democratic opponent, “really has no experience or knowledge or judgment about the issue of Iraq and he has wanted to surrender for a long time”.

He contrasted his own eight trips to Iraq with that of Mr Obama, who made his only visit in 2006, and even offered to take the Democrat on his next visit to help to educate him about how far security has improved. The Obama campaign dismissed the offer as “political posturing”.

The two candidates are tracking each other across the southwestern region, which campaign strategists have identified as a key battleground in November. On Monday both were in New Mexico. Mr Obama swung through Nevada yesterday before heading to Colorado today. Mr McCain is matching him every step of the way, with a visit to Colorado yesterday and Nevada today.

In his speeches, Mr Obama regularly accuses Mr McCain of seeking a “Bush third term” and yesterday he relished the chance to highlight the furtive nature of the fundraiser in Arizona. “No cameras. No reporters,” he said. “And we all know why. Senator McCain doesn’t want to be seen, hat-in-hand, with the President, whose failed policies he promises to continue for another four years.”

Recent Democratic television advertising portrays Mr McCain with Mr Bush, alongside the message: “Can you tell ’em apart?”

The Republican Congressman Tom Davis has set out a 20-page campaign memo recently, saying that the President is “absolutely radioactive” for the party. “It starts with the brand,” he stated, “and the brand is Bush.”

Even Mr Bush has observed that Mr McCain, with whom he fought a tempestuous battle for the Republican nomination in 2000, wants to “distance himself from me a little bit”.

Mr McCain has sought to reinforce his credentials as a maverick reformer by introducing a new rule requiring the resignation of any member of his campaign team who is an active lobbyist. But his efforts to avoid being tainted by the President are constantly tempered by his need to reassure the conservative base of his party.

Mr McCain mixes speeches on global warming aimed at independent voters with appearances at organisations such as the National Rifle Association, which has criticised him for allegedly liberal views on gun control.

Nor, as last night’s event proved, can he afford to alienate the Republicans’ loyal donors, whose wallets Mr Bush has always been adept at opening. Although the Republican presidential candidate had his most lucrative month yet in April, raising $18 million (£9 million), Mr Obama routinely receives more than $30 million.

The Bush fundraising machine may yet be Mr McCain’s best hope. The latest figures show the Republican National Committee has more than $40 million, ten times more than its Democratic counterpart.

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