In a speech late Friday to a powerful conservative lawyers' association, Cheney said a retreat would encourage terrorist violence.
"Some in our country may believe in good faith that retreating from Iraq would make America safer. Recent experience teaches the opposite lesson," he said.
"To get out before the job is done would convince the terrorists, once again, that free nations will change our policies, forsake our friends and abandon our interests whenever we are confronted with violence and blackmail."
Cheney was speaking to the Federalist Society 10 days after opposition Democrats won control of Congress in legislative elections that were fought out in part over the continuing presence of more than 140,000 US troops in Iraq.
Opinion polls before the November 7 vote showed that a large majority of Americans wanted to begin pulling back in the face of a rising death toll for US troops in the country.
More than 2,800 US soldiers have died in the country since the US-led coalition invasion in March 2003, with October one of the bloodiest months to date.
Immediately after the elections the Democrats, with the support of some Republicans, began pushing the White House for a timetable for withdrawal, with Democrat House of Representatives leader Nancy Pelosi saying the US force presence in Iraq only exacerbates the problem of violence there.
But even as the White House began considering the views of a high-powered review board on Iraq policy, Cheney adamantly insisted Friday that pulling US troops out early would be a mistake.
"America is going to complete our mission, get it done right, and bring our troops home in victory," he said.
"There's still tough work ahead, and as the enemy switches tactics we are doing the same ... The key is to get Iraqis into the fight, and we'll continue training local forces so they can take the lead in defending their own country."
Cheney's view was echoed by President George W. Bush, who on a visit to Vietnam Friday said that one lesson of the bloody US military defeat there a generation ago was that the United States must be patient in Iraq.
"We'll succeed unless we quit," Bush promised.
Asked whether the US defeat in Vietnam offered lessons, the US president replied: "We tend to want there to be instant success in the world, and the task in Iraq is going to take a while."
Meanwhile on Friday several lawmakers said that the Pentagon plans to ask Congress for 127 billion dollars for the wars in Iraq and Afghanistan in 2007 in addition to 70 billion dollars already budgeted.
Senator Kent Conrad's office confirmed that he understood the supplemental budget request would be around 127 billion dollars, while USA Today newspaper cited Democratic Representative Jim Cooper as putting the figure at up to 160 billion dollars.

Copyright AFP (Agence France-Presse), 2006