(Updates with Cheney, Bush, Kerry) By Tabassum Zakaria WASHINGTON, Oct 19 (Reuters) - U.S. President George W. Bush says he sees a possible parallel between the increase in violence in Iraq and the 1968 Tet offensive that prompted a loss of support among Americans for the Vietnam War. But the White House on Thursday said the president was not making the analogy that Iraq had reached a similar turning point. Instead, he meant that insurgents might be increasing violence to try to influence the upcoming U.S. election. Bush was asked in an ABC News interview on Wednesday whether he agreed with New York Times columnist Thomas Friedman's opinion that the violence in Iraq was "the jihadist equivalent of the Tet offensive." Bush responded: "He could be right. There's certainly a stepped-up level of violence, and we're heading into an election." Bush and other top U.S. officials have long resisted comparisons to the Vietnam War when critics have suggested that Iraq has turned into a quagmire. But They have stepped back from adamant declarations of progress as sectarian violence ratchets up, with more than 2,750 American troops and tens of thousands of Iraqis killed since the U.S.-led invasion in March 2003. Attacks in Iraq killed about 40 people on Thursday. The death toll for U.S. troops rose to 72 for October, which could become one of their deadliest months in two years. "I expressed the sentiment some time ago that I thought we were over the hump in terms of violence, I think that was premature," Vice President Dick Cheney said in an interview with TIME magazine. Cheney agreed that insurgents were trying to create as much bloodshed as possible to influence public opinion in the United States. Communist forces lost the Tet offensive, but it was a major propaganda victory and is widely considered a turning point of the war in Vietnam, prompting support among Americans for the conflict to drop. President Lyndon Johnson's popularity fell and he withdrew as a candidate for re-election in March 1968. White House spokesman Tony Snow said Bush was not trying to say that the surge in violence was a turning point in Iraq. "We do not think that there's been a flip-over point," he said. MORE FLEXIBLE TONE Bush has taken a more flexible tone on Iraq, saying he is open to adjusting policy, as the Nov. 7 elections approach with his Republican Party facing the possibility of losing control of the U.S. Congress because of the unpopular war. He has maintained that Iraq is not embroiled in civil war and continues to insist that U.S. troops will not leave until Iraqis can take over their own security. "There is one thing we will not do. We will not pull out our troops from Iraq before the terrorists are defeated," Bush said on Thursday at a Republican fund-raiser where he accused Democrats of seeking to retreat instead of win. Sen. John Kerry, a Massachusetts Democrat, called Bush's Iraq policy wrong and said U.S. military efforts should be focused on tracking down and killing members of al Qaeda. "This is the opposite of President Bush's stand-still-and-lose strategy," he said in a statement. Bush told ABC that not every American soldier would be out of Iraq before he leaves office in January 2009. There are about 144,000 U.S. troops currently in Iraq. "Look, here's how I view it," Bush said. "First of all, al Qaeda is still very active in Iraq. They are dangerous. They are lethal. They are trying to not only kill American troops, but they're trying to foment sectarian violence. "They believe that if they can create enough chaos, the American people will grow sick and tired of the Iraqi effort and will cause government to withdraw." (Additional reporting by Steve Holland)