"They will be there until there is full compliance," Cohen said Thursday.
Once the additional aircraft, ships and air units arrive sometime this weekend, about 30,000 American soldiers, sailors, airmen and Marines will be in the region.
For his part, President Clinton said he would hold to a "wait and see" approach to determine whether Iraq allows U.N. weapons inspectors to resume work.
"This is not over," declared Sandy Berger, the president's national security adviser.
Three weeks after triggering an international showdown, Saddam on Thursday suddenly revoked his ban on American weapons inspectors in Iraq.
Inspectors arrived in Baghdad early today after a flight from Bahrain. "We will start our inspections as soon as possible," Maj. Gen. Nils Carlstrom, the Swede who heads the Baghdad monitoring office, said in a statement before the weapons inspectors left Bahrain.
But underscoring U.S. skepticism about Iraq, the Pentagon continued its buildup, dispatching F-16 and F-15 fighters, B-1 long-range bombers, refueling planes and soldiers to man Patriot air defense missiles.
"The forces will stay as long as they are necessary to be there to make sure that our own forces are protected," Cohen said.
During the extended crisis over the inspections, the allied countries that had defeated Saddam in the 1991 Gulf War showed divisions over whether to use force to compel Iraqi compliance.
Whether the allies will remain united in their resolve to enforce U.N. sanctions that were imposed on Saddam following his 1990 invasion of Kuwait may be tested as early as today when a U.N. special commission meets to make arrangements for inspections.
Russia, with some French support, may try to narrow the monitoring for Iraqi weapons of mass destruction. Saddam has contended the U.S. inspectors were actually spies.
The White House insisted Saddam got nothing for backing down. Officials emphasized that the United States stood ready to veto any efforts by Russia or others to ease the economic and military sanctions.
"There is absolutely no understanding. There's no deal. There's no concessions," Berger said at a White House briefing.
However, officials also said the United States would support increasing the amount of oil Iraq is permitted to sell to raise money to buy food and medicine.
Clinton, at a prayer breakfast with religious leaders Thursday, said, "The United States must remain and will remain resolute" in preventing Saddam from developing nuclear, chemical or biological weapons. "In the coming days we will wait and see whether he does, in fact, comply with the will of the international community."
Iraq reversed course under an arrangement brokered by Russia, which promised to press for the lifting of sanctions. Iraqi Deputy Prime Minister Tariq Aziz said Russia had promised to work for a "just and fair diplomatic solution." But he acknowledged that the U.N. Security Council's permanent members had offered no specific commitments.
The United States declared it was not party to the Russian deal. "It is not binding on us or on the U.N.," Berger said. "It is not something that we are obligated to in any respect, or the U.N."
The United States said U-2 spy planes that Saddam had threatened to shoot down would continue to fly over Iraq and that Americans would remain part of the weapons inspection team.
"There should be no attempt and no expectation that there will be any change in either composition of inspectors or flights that may be flown or any material change in the inspection regime that is required," Cohen said.
The United States was concerned that the expulsion of inspectors allowed Iraq to make some advances in its weapons programs. Berger said the United Nations would not be able to assess what had happened until its inspectors were allowed to go back to work.
Even so, Berger said Saddam "can't reconstitute in a matter of a few weeks what (U.N. inspectors) have been successful in destroying" over the past six years. Yet, he said there was "obviously some loss as each day went _ goes by."