Cheney deliberately softened his tone of earlier in the week when he said allowing inspections would only give Saddam more time to work on his weapons of mass destruction.
There was reportedly concern that the vice president made it sound as though the U.S. had already decided there was no alternative to war.
Instead, the message the administration wants to send is that the president will consult with the allies and congress - and make his case to the American people - before taking action.
Cheney took his arguments for launching a pre-emptive war on Iraq before another group of U.S. veterans today, this time in San Antonio, Texas.
As CBS News Correspondent Bill Plante reports, some listeners detected a slight softening of Cheney's hawkish stand, or at least an acknowledgement that there are other valid points of view worth debating.
"Many have suggested that the problem could be dealt with by simply returning inspectors to Iraq. But we must remember that inspections are not an end in themselves. The objective has to be disarmament," said the vice president.
Meanwhile, despite the determination of White House lawyers that congressional approval is not needed for an attack on Iraq, President Bush's advisers have concluded that it would be prudent to seek some sort of expression of support from lawmakers if he decides on military action.
Officials told The New York Times there was widespread acknowledgment that it would be unwise to launch an attack without support from Congress.
One official suggested that the assertions about congressional approval being unnecessary were "like the opening round in a negotiation" with lawmakers, meant to make Congress more pliable on the wording of any potential statement of support.
Intense debate also is under way within the administration on whether to seek a U.N. Security Council vote declaring that Iraqi President Saddam Hussein must readmit weapons inspectors.
Earlier, Sen. John Warner of Virginia, the top Republican on the Senate Armed Services committee, became the latest GOP lawmaker to insist that Congress be heard in the debate on whether to invade Iraq.
"Congress, as a co-equal branch of government, is, in my opinion, not going to sit on the sidelines," Warner said in a letter to committee chairman Sen. Carl Levin, D-Mich. The letter was dated Tuesday and released Wednesday.
Warner said Wednesday he wants Defense Secretary Donald H. Rumsfeld to appear before the panel to discuss how prepared U.S. forces are for a war against Iraq.
Warner said the time has come for the committee to hold hearings on Iraq after the congressional recess ends next week. He said the first witnesses should be administration officials — preferably Rumsfeld and Joint Chiefs of Staff Chairman Gen. Richard Myers.
In a statement Wednesday, Levin said he has been considering holding hearings on Iraq and would decision after the recess.
Pentagon spokeswoman Victoria Clarke said Rumsfeld expects to be asked to testify next month and is prepared to do so.
Speaking in Crawford, Texas, where the president is vacationing, White House spokesman Scott McClellan said hearings would be "part of a healthy discussion about how we move forward on Iraq."
Warner said "there appears to be a 'gap' in the facts possessed by the executive branch and the facts possessed by the legislative branch."
In an interview, Warner said his reference to the gap wasn't meant to criticize the administration, but to acknowledge that administration officials are constantly gathering intelligence, making assessments and conferring with foreign leaders.
Warner noted that "the crescendo of this debate (on Iraq) has risen dramatically in the last two weeks."
U.S. allies have increasingly urged the United States against an attack. On Wednesday, a senior Turkish diplomat cautioned that an attack could lead to the breakup of Iraq. Turkey serves as the base for U.S. and British surveillance flights over Iraq.
Asked about widespread opposition to military action against Iraq, State Department spokesman Richard Boucher reaffirmed that Mr. Bush has not yet made a decision.
"The president made clear we'll continue to talk to other governments and consult with them, hear their views, as he decides how to go forward," Boucher said.