But some diplomats have said they doubt the latest statement by the five states is strong enough to placate their critics.
The United States, Russia, Britain, France and China reaffirmed their "unequivocal commitment" to the ultimate goal of scrapping their stockpiles of weapons.
But their statement, issued at a UN conference on nuclear non-proliferation, gave no timetable and was derided as a platitude by environmentalists.
The five countries said that none of their missiles was targeted at any other state - something they have announced individually in the past.
The BBC United Nations correspondent says non-nuclear states believe the big five have squandered the opportunity offered by the end of the Cold War for the complete dismantling of the nuclear arsenals.
Goal-setting
The United States and Russia have come in for particular criticism - with an estimated 20,000 or more warheads between them.
They have already agreed to reduce their arsenals to between 2,000 and 2,500 by the year 2007.
The aim of the Nuclear Non-proliferation Treaty (NPT) conference in New York, which ends on 19 May, is to set goals for the 187 signatories to the NPT for the next five years.
But some diplomats have said they doubt the latest statement by the five states is strong enough to placate their critics.
Monday's statement calls for "preserving and strengthening" the 1972 US-Russian Anti-Ballistic Missile treaty, which the Clinton administration wants to amend to accommodate plans for a national ballistic missile defence shield.
Exclusive club
In May 1995, non-nuclear states agreed to an indefinite extension of the 1970 NPT in exchange for a commitment from the five nuclear weapons states to negotiate "in good faith" towards nuclear disarmament.
Israel, India, Pakistan and Cuba all refused to sign the NPT.
They regard the treaty as an attempt to set in stone the strategic superiority of the five major nuclear powers.
Under the treaty, only these five nations are permitted to possess nuclear weapons.
The other 182 signatories have renounced nuclear weapons for good.
'Not going far enough'
Darach MacFhionnbhairr, an Irish government delegate to the five-year review of the NPT, said the statement was flawed because it was "a commitment for some indefinite future period."
Environmental campaign group Greenpeace dismissed it as "a lame attempt to excuse the inexcusable: the failure of the nuclear-weapons states to take meaningful action on disarmament."
The statement would heighten the concern of other states which feared that the action of the five leading nuclear powers "will be limited to platitudes," said William Peden of Greenpeace.