WASHINGTON - The United States is safer now than it was before the Sept. 11 attacks, but must not relent in fighting terrorism in Iraq and elsewhere, Secretary of State Condoleezza Rice said Sunday.

In this photo provided by FOX News, Secretary of State Condoleezza Rice appears on 'Fox News Sunday' in Washington, Sunday, Sept. 10, 2006. [AP]

"I think it's clear that we are safe - safer - but not really yet safe," said Rice, who was President Bush's national security adviser when al-Qaida masterminded the attacks of Sept. 11, 2001.

Yet Democratic leaders said the Bush administration has gotten the U.S. bogged down in Iraq when there was no evidence of links to the Sept. 11 attacks, detracting from efforts against al-Qaida and other terrorist groups.

"I think we're in trouble," said Howard Dean, chairman of the Democratic National Committee.

A poll released Sunday found that 55 percent of those surveyed think the country is safer from terrorism than it was before Sept. 11, 2001, while 37 percent do not. The ABC News poll also said 38 percent think the government is doing all it can to prevent another terrorist attack, while 60 percent say it is not.

Vice President Dick 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-Qaida operative Abu Musab al-Zarqawi or his associates.

Rice, however, maintained "there were ties between Iraq and al-Qaida. 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 Sept. 11 plot. "If you think that 9/11 was just about al-Qaida 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," Rice.

Meantime, the U.S. 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 Sept. 11," John Negroponte wrote in Sunday's Washington Post.

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

A Republican member of the commission that investigated the Sept. 11 attacks said the U.S. 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-Qaida, 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 the administration should do more to secure ports, chemical plants and other potential sites of homeland terrorism.

"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," Dean said. "What we ought to be doing is going after Osama bin Laden full-scale."

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