George Bush is expected shortly to ask the Pentagon to reassess its nuclear arsenal with a view to possibly cutting the number of American nuclear warheads by well over half.

The President acknowledged yesterday that he will ask the Defence Secretary, Donald Rumsfeld, to begin a "top-to-bottom review" of the US military and of its spending.

Mr Bush made no direct comment about unilateral cuts in nuclear weapons but officials indicate that will become a priority.

President Bush alluded often during his election campaign to scaling back the nuclear arsenal.

Large cuts could also help to assuage concerns in China, Russia and among the European allies about US plans for a nuclear missile shield, known as the National Missile Defence programme.

"The review, I understand, could be a step toward a new strategic doctrine," one senior defence source said. "We would balance strong defence with a smaller nuclear offence – unlike the massive number of warheads during the Cold War."

Answering reporters' questions yesterday, Mr Bush confirmed that the military is to reassess itself. "Secretary Rumsfeld is beginning a review of the defence – a top-to-bottom review of what's happening in today's military, reviewing missions, reviewing opportunities for change," he said at the White House.

The US currently has about 7,000 nuclear warheads while Russia has 6,000. The latest arms control treaties between Washington and Moscow call for levels to fall to between 2,000 and 2,500 for each side. Mr Bush could seek to cut these levels even further.

Analysts suggest that a unilateral reduction in its nuclear arsenal will give the US room to back away from the 1972 Anti-Ballistic Missile treaty. At present the ABM, considered a foundation stone of disarmament, would stand in the way of the US building or even testing a missile defence shield.

Cutting the nuclear capability would also allow Mr Bush to reinforce the US military in other ways, with new conventional weaponry and a boost in pay for US personnel.

He said that pay rises and other defence priorities would be one of the issues he will discuss while "travelling the country next week".

Mr Rumsfeld has also kept his counsel on the nuclear weapons question. But asked by reporters recently about the prospect of a sharply reduced US nuclear arsenal, he noted that, "it is a different world, we know that".

President Bush's insistence on a comprehensive review of all military priorities has not won him praise from all quarters of the Pentagon.

Many in the military would like Mr Bush to commit more money to the US armed forces now before starting the reassessment.

Mr Bush stressed yesterday, however, that there would be no "early supplemental" for the Pentagon, meaning that he would not seek any early increase in the current Pentagon budget of $297bn (£205bn).

Aides say that he could ask for additional defence money from Congress in the summer.

Some senior US officers have also expressed deep reservations about any unilateral cuts in America's nuclear strike force while Russia retains its full arsenal.

Last year, however, senior officials from the Pentagon conceded during hearings in Congress that US defence needs could easily be met with a much reduced number of missiles.

Next week, Mr Bush is to travel with Mr Rumsfeld to several US military bases, including the US Joint Forces Command in Virginia.