George Bush's three-day visit to London next week is prompting tension between US security agents and Ken Livingstone.
Protesters want to march through central London
American officials are demanding an exclusion zone round the president, while the London mayor wants to keep the city as "open as possible".
Police are planning a £4m security operation to cope with an estimated 100,000 anti-war protesters.
Scotland Yard says it will facilitate lawful demonstrations, but campaigners suspect they will not be allowed to march through Whitehall, Parliament Square or the Mall.
Road closures will not be revealed until the last minute for security reasons, say police.
However Mr Livingstone dismissed any notion that wide swathes of central London would be closed.
"The ideas of some American security advisers that perhaps we should shut the whole of central London for three days, ignoring the economic consequences of that, I don't think that's got a chance at all," he said.
Mr Livingstone said the fact no prime minister had been assassinated in nearly two centuries showed the British had always had good security.
It will be Mr Bush's first visit to London since July 2001, which was met with some protest but little disruption.
But in the wake of the 11 September terror attacks and large demonstrations in London against the war in Iraq, police are facing a huge security operation.
Jeremy Corbyn, MP for Islington North and a Stop the War activist, told BBC Radio 4's Today programme: "We've had long discussions with the police and one gets the feeling that there is a bigger hand somewhere that is trying to prevent a march going along Whitehall and past Parliament Square.
Disruption 'kept to a minimum'
"The Americans are actually running the security operation in London as well... I'm getting a bit alarmed about the degree of invasion of our capital by the Americans.
"The idea of closing off large parts of London to ensure that President Bush is taken well away from any protests or demonstrators seems a little insensitive and an enormous inconvenience to an awful lot of people."
Metropolitan Police Commissioner Sir John Stevens said: "Because of the security implications we won't be announcing the road closures until the last minute.
"We will keep those to a minimum, we must make sure London continues to operate as normally as possible."