Republican and Democratic lawmakers made demands Tuesday for a quick test of President Saddam Hussein's promise to allow U.N. weapons inspectors unfettered and unconditional access throughout Iraq.

Some senators remained deeply skeptical of the accord reached by Secretary-General Kofi Annan of the United Nations and Saddam, and most said they still needed to review the fine print.But a growing number of legislators expressed guarded optimism as they were briefed by senior officials of the Clinton administration about the accord's highlights.

"I strongly support the initiative the president has taken," said Speaker Newt Gingrich of Georgia, "and my hope is that we will learn in the next day or two that it is a good agreement and an enforceable agreement and one that has automatic consequences if Saddam breaks his word."

All day President Clinton's top national security officials fanned out on Capitol Hill to explain the agreement to senators as best they could. Administration officials are to brief the House on Wednesday.

Senior administration officials said on Tuesday evening that Clinton had spoken to Annan on Tuesday about some of the confusion in the document Anna negotiated with the Iraqis. Annan assured the president that diplomats who would be part of a special group inspecting presidential sites would merely accompany the weapons experts. Secondly, Annan said that the commissioner he would appoint to head the special group would already be working for the inspection commission. Thirdly, Annan assured Clinton that the commission would retain its current relationship to the Security Council. Other issues remained to be clarified, officials said.

House and Senate members demanded that Saddam's pledges, which have been broken in the past, be tested immediately to see whether the Iraqi leader will abide by his promises and to determine how much longer the United States should keep a military force of 32,000 in the Persian Gulf region.

"We hope there will be an early test to see if Saddam Hussein is going to keep his word," said Sen. Trent Lott of Mississippi, the majority leader. "He has a long record of lying and cheating on these inspections."

Sen. Lauch Faircloth, R-N.C., said, "We have to hold the force there until the inspections are done."

Since the showdown with Saddam over weapons inspections began in November, the United States has nearly doubled the size of its forces in the region. There are now 20 warships in the gulf and nearly 400 aircraft aboard carriers and in Saudi Arabia, Kuwait and Bahrain.

Lawmakers complained that the buildup was costly and diverted aircraft carriers from the Western Pacific and the Mediterranean.