No matter who is president, the country is vulnerable to attack, he said in a newspaper interview.
On Tuesday, Cheney told supporters in Iowa that there's a danger the United States will be attacked again "if we make the wrong choice" on Election Day.
Democrats and others pounced on the vice president, with Democratic opponent John Edwards calling Cheney's comments undignified and divisive. President Bush declined to respond when he was asked whether he agreed with his running mate.
In an interview Thursday with the Cincinnati Enquirer, Cheney sought to clarify those remarks, saying he wanted to "clean up" the controversy.
"I did not say if Kerry is elected, we will be hit by a terrorist attack," Cheney told the newspaper, according to a story prepared for Friday's editions. "Whoever is elected president has to anticipate more attacks. My point was the question before us is: Will we have the most effective policy in place to deal with that threat? George Bush will pursue a more effective policy than John Kerry."
On Tuesday, campaigning in Iowa, Cheney had said: "It's absolutely essential that eight weeks from today, on Nov. 2, we make the right choice, because if we make the wrong choice then the danger is that we'll get hit again and we'll be hit in a way that will be devastating from the standpoint of the United States."
Cheney was in Cincinnati for a "town hall" meeting with about 500 invited supporters. In the public forum, Cheney did not address his earlier remarks, though he offered some of the same context he had given Tuesday, saying the United States cannot view terrorism as it views ordinary crime.
At the town hall session, Cheney answered about a half-dozen friendly questions in this conservative section of this contested swing state.
He vigorously defended the U.S. invasion of Iraq, once again drawing a link between Saddam Hussein and al Qaeda terrorists that is disputed by experts, including the bipartisan Sept. 11 commission.
The vice president skimmed over President Bush's principal justification for going to war: that Saddam harbored weapons of mass destruction and planned to use them. No such weapons were found in Iraq.
The bipartisan commission that investigated the attacks cited contacts between Saddam's regime and al Qaeda chief Osama bin Laden, but said there was no "collaborative operational relationship" and said Iraq was not involved in the Sept. 11 terrorist strikes.
Cheney recounted the invasion of Afghanistan in 2001, in which the United States punished the Taliban for harboring al Qaeda, which is blamed for the Sept. 11 attacks. Then he said, "In Iraq, we had a similar situation."
Saddam, he said, "provided safe harbor and sanctuary for terrorists for years," including al Qaeda.
Cheney was probably referring to Abu Musab al-Zarqawi, a Jordanian-born terrorist with alleged links to bin Laden. Before the invasion, the administration accused Saddam of harboring al-Zarqawi, but outside experts are not convinced of the strength of those ties.
Cheney also talked up the economy. He said national employment statistics miss many people who are making money, such as those selling items on eBay.
"That's a source that didn't even exist 10 years ago," he said. "Four hundred thousand people make some money trading on eBay." It's unclear how many of those are making enough to support themselves.
Cheney said he and Bush are committed to simplifying the tax code, but would not commit to any particular plan when asked about a national sales tax or flat income tax. Bush recently said the idea of a national sales tax should be explored.
Cheney added Russia to his list of countries that have suffered from terrorism, speaking of the school hostage crisis that left more than 300 dead. He suggested there may be ties between Chechen terrorists who have been fighting Russian forces for years and al Qaeda, saying some of them trained at camps in Afghanistan.
"There may be some links there but we just don't have specific details," he said.
Cincinnati is in heavily Republican Hamilton County, won by Bush with nearly 56 percent of the vote in 2000, his largest margin of victory among Ohio's 88 counties.
Bush has been to Ohio 24 times since taking office. Kerry has visited 15 times this year.
Later, Cheney spoke at a fund-raising dinner in Green Bay, Wis., that was to net $250,000 for the Republican National Committee.