BAGHDAD — Vice President Cheney warned yesterday against large American troop cuts that could jeopardize recent security gains in Iraq, as he marked the fifth anniversary of the American-led invasion with a two-day visit to the country.

Mr. Cheney used words like “phenomenal” and “remarkable turnaround” to describe a drop in violence in Iraq, and he hailed recently passed legislation aimed at keeping Iraq on a democratic path.

“It would be a mistake now to be so eager to draw down the force that we risk putting the outcome in jeopardy, and I don’t think we’ll do that,” Mr. Cheney said after spending the day zigzagging through barricades and checkpoints to get to meetings in and out of the heavily guarded Green Zone. He spent the night at an American military base, the second overnight stay in Iraq for the vice president — the highest-ranking official to do so. Reporters accompanying him were not allowed to disclose the location. Last May, Mr. Cheney stayed at Camp Speicher, a base near former leader Saddam Hussein’s hometown and about 100 miles north of Baghdad.

“It is good to be back in Iraq,” Mr. Cheney, dressed in a suit and dark cowboy boots, said after his meeting with Prime Minister al-Maliki. “It’s especially significant, I think, to be able to return this week as we mark the fifth anniversary of the beginning of the campaign that liberated the people of Iraq from Saddam Hussein’s tyranny, and launched them on the difficult but historic road to democracy.”

He acknowledged that there is still a lot of difficult work to be done in Iraq, where 160,000 troops are deployed and the American death toll is about to top 4,000. His own motorcade, escorted by Humvees manned by troops with machine guns, never ventured farther than about a mile outside the Green Zone.

“But as we move forward, the Iraqi people should know that they will have the unwavering support of President Bush and the United States in consolidating their democracy,” Mr. Cheney said.

Security has improved markedly since last summer, when the last of five Army brigades arrived in Iraq to complete the president’s buildup of 30,000 troops. One brigade has already returned home and the four others are to leave by July. What remains unclear is whether Mr. Bush will order additional drawdowns in the final months of his presidency.

Mr. Bush’s decision last January to increase troops put to rest any notion, “here inside Iraq or in the region, that people could ‘wait us out,'” Mr. Cheney said.