Bush said in a speech to the Israeli Knesset: "Some seem to believe we should negotiate with terrorists and radicals, as if some ingenious argument will persuade them they have been wrong all along.
"We have heard this foolish delusion before.
"As Nazi tanks crossed into Poland in 1939, an American senator declared: 'Lord, if only I could have talked to Hitler, all of this might have been avoided.'
"We have an obligation to call this what it is: the false comfort of appeasement, which has been repeatedly discredited by history."
The senator Bush referred to was William Borah, a Republican from Idaho.
Obama, the front-runner for the Democratic presidential nomination, bristled at Bush's remarks.
"It is sad that President Bush would use a speech to the Knesset on the 60th anniversary of Israel's independence to launch a false political attack," Obama said in a statement.
Obama added: "George Bush knows that I have never supported engagement with terrorists, and the president's extraordinary politicization of foreign policy and the politics of fear do nothing to secure the American people or our stalwart ally Israel."
Obama has called for high-level talks with the leaders of Iran and Syria but has staunchly opposed meeting with Hamas, which controls Gaza and which the U.S. and Israel have labeled a terrorist organization.
Clinton, Obama's rival for the nomination, defended him, although she has in the past criticized his stance on talking with the nation's adversaries. She labeled Bush's remarks "offensive and outrageous, especially in light of his failures in foreign policy."
McCain, the presumptive Republican presidential nominee, joined the fray in Columbus, Ohio.
"This does bring up an issue that we will be discussing with the American people, and that is: Why does Barack Obama, Sen. Obama, want to sit down with a state sponsor of terrorism?" he said.
Obama spokesman Tommy Vietor retorted: "It is the height of hypocrisy for John McCain to deliver a lofty speech about civility and bipartisanship in the morning and then embrace George Bush's disgraceful political attack in the afternoon."
Other prominent Democrats, including Rep. Rahm Emanuel of Illinois, Sen. Joseph R. Biden Jr. of Delaware and House Speaker Nancy Pelosi of San Francisco, accused the president of delivering partisan remarks in an inappropriate setting.
This report includes information from Chicago Tribune news services.