Senate Majority Leader Bill Frist, R-Tenn., said the statement by the Massachusetts senator called into question Kerry's fitness to be the nation's chief executive.
"Free and open discourse is one thing, but petty, partisan insults launched solely for personal political gain are highly inappropriate at a time when American men and women are in harm's way," Frist said in a statement Thursday.
In a speech Wednesday in Peterborough, N.H., Kerry said President Bush so alienated allies prior to the U.S.-led war against Iraq that only a new president can rebuild damaged relationships with other countries.
"What we need now is not just a regime change in Saddam Hussein and Iraq, but we need a regime change in the United States," Kerry said.
House Speaker Dennis Hastert, R-Ill., said that in the midst of war, the nation should pull together to support the troops and commander in chief.
"Once this war is over, there will be plenty of time for the next election," he said in a statement.
House Majority Leader Tom DeLay, R-Texas, also issued a statement, calling Kerry's words "desperate and inappropriate."
"America before New Hampshire," DeLay said.
Kerry dismissed the criticism, saying patriotism is not mutually exclusive with questioning the war.
"I don't need any lessons in patriotism or in caring for America," Kerry, a decorated Vietnam veteran, told Democrats at a meet-the-candidates dinner in Atlanta. "We're fighting for the rights of Americans…I speak out for America, not for politics."
Neither Hastert, Frist nor DeLay served in the military. Mr. Bush served in the Texas National Guard.
After speaking to the New York State United Teachers convention in Washington Friday morning, one of Kerry's Democratic rivals, former Vermont Gov. Howard Dean, said he probably would not have used the words that Kerry did, but, "I have not criticized Senator Kerry for that, nor am I going to.
"It certainly would be unusual for me to line up with Tom DeLay, and I don't intend to start now," said Dean, who in recent weeks has assailed Kerry, suggesting that the lawmaker has waffled on the issue of the war.
Kerry backed a congressional resolution last fall giving Mr. Bush the authority to use force to oust Saddam, but he repeatedly has criticized the president for failing to give diplomacy more time.
Leading congressional Democrats generally have avoided criticism of Mr. Bush since U.S.-led forces began attacking Iraq.
On March 17, when Mr. Bush announced that military strikes would begin against Iraq unless Saddam left the country, Senate Minority Leader Tom Daschle, D-S.D., said Mr. Bush's diplomatic efforts had failed "miserably" because he didn't secure a U.N. resolution for the war.
Daschle's remarks drew a sharp rebuke from Hastert and DeLay. This week, Daschle said he was satisfied with Mr. Bush's strategy.
Traditionally, politicians mute criticism of a president's foreign policy once war in underway. But there have long been exceptions. Sitting senators were among the leading critics of the Vietnam War.