WASHINGTON — America is safer now than it was before the September 11, 2001, attacks but must not relent in fighting terrorism in Iraq and elsewhere, Secretary of State Rice said yesterday.

“I think it’s clear that we are safe — safer — but not really yet safe,” Ms. Rice, who was President Bush’s national security adviser when the attacks occurred, said.

Yet Democratic leaders said the Bush administration has gotten America bogged down in Iraq when no evidence existed of links to the September 11 attacks, detracting from efforts against Al Qaeda and other terrorist groups.

“I think we’re in trouble,” the chairman of the Democratic National Committee, Howard Dean, said.

A poll released yesterday found that 55% of those surveyed think the country is safer from terrorism than it was before September 11, while 37% do not. The ABC News poll also said 38% think the government is doing all it can to prevent another terrorist attack, while 60% say it is not.

Vice President Cheney defended the invasion of Iraq but acknowledged that the insurgency was not “in its last throes,” as he said in May 2005. “I think there is no question but that we did not anticipate an insurgency that would last this long,” he said.

A Senate report released Friday disclosed for the first time that a CIA assessment in October 2005 said Saddam’s government “did not have a relationship, harbor, or turn a blind eye toward” Al Qaeda operative Abu Musab al-Zarqawi or his associates.

Despite this information, Ms. Rice maintained that “there were ties between Iraq and Al Qaeda. Now, are we learning more now that we have access to people like Saddam Hussein’s intelligence services? Of course, we’re going to learn more.”

She said that, “as far as we know,” Saddam had no knowledge of or role in the September 11 plot. “If you think that 9/11 was just about Al Qaeda and the hijackers, then there’s no connection to Iraq. But if you believe, as the president does and as I believe, that the problem is this ideology of hatred that has taken root, extremist ideology that has taken root in the Middle East, and that you have to go to the source and do something about the politics of that region. It is unimaginable that you could do something about the Middle East with Saddam Hussein sitting in the center of it, threatening his neighbors, threatening our allies, tying down American forces in Saudi Arabia,” Ms. Rice said.

Meanwhile, the American intelligence chief said that, over the past five years, the country has made major gains in “connecting the dots” about threats by sharing information among intelligence agencies.

“The American people should understand that the components of the nation’s intelligence community are working together in ways that were almost unimaginable before September 11,” John Negroponte wrote in yesterday’s Washington Post.

According to recent AP-Ipsos polling, half of people residing in America say they feel the cost of fighting terrorism may be too high, and 45% say they have less faith in the government’s ability to protect them. Also, just over half have little confidence that Osama bin Laden will ever be caught.

A Republican member of the commission tasked with investigating the September 11 attacks said the country has taken important steps to stem terrorism by capturing many of those responsible for the planning.

“We have gotten rid of most, if not all, theater commanders of Al Qaeda, but we have not addressed, as a nation, the root cause … this jihadist ideology that is being preached around the world, basically funded with Persian Gulf money,” John Lehman said.

Democrats contend that the administration should do more to secure ports, chemical plants, and other potential sites of attack.

“We have not pursued the war on terror with the vigor that we should have because we’ve gotten bogged down in this civil war in Iraq,” Mr. Dean said. “What we ought to be doing is going after Osama bin Laden full-scale.”

Ms. Rice appeared on CNN’s “Late Edition,” CBS’s “Face the Nation,” and “Fox News Sunday,” where Mr. Dean was interviewed, too. Mr. Cheney was on NBC’s “Meet the Press” and Mr. Lehman on ABC’s “This Week.”