Mr Obama accused Mr Bush a "launching a political attack"
Barack Obama has accused George W Bush of attacking him after the US president compared those in favour of talking to terrorists to Nazi appeasers.
The White House has denied that the remarks - from a speech to the Israeli parliament - were aimed at Mr Obama.
Mr Obama, who is the frontrunner to become the Democrats' presidential nominee, has argued in favour of negotiating with the Iranian regime.
But he has ruled out talking to militant organisations like Hamas.
"Some seem to believe that we should negotiate with the terrorists and radicals," said Mr Bush in his speech.
"We have heard this foolish delusion before. As Nazi tanks crossed into Poland in 1939, an American senator declared: 'Lord, if I could only have talked to Hitler, all this might have been avoided.' We have an obligation to call this what it is - the false comfort of appeasement."
Mr Obama responded in a statement:
"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. George Bush knows that I have never supported engagement with terrorists."
But White House spokeswoman Dana Perino rejected Mr Obama's interpretation of the president's remarks, saying "there are many who have suggested these types of negotiations with people that the president... thinks that we should not talk to".
"I understand when you're running for office you sometimes think the world revolves around you," she added.
"That is not always true. And it is not true in this case."
The BBC's James Coomarasamy in Washington says the row indicates that Republicans have identified Senator Obama's Middle East policy and his perceived weakness amongst Jewish voters as a key point of attack, should he, as many expect, be Republican John McCain's opponent in the November election.
Mr Obama raised eyebrows last year when he first stated his support for direct negotiations without preconditions with the controversial Iranian President, Mahmoud Ahmadinejad.
His position has been criticised, not only by John McCain, but also by Mr Obama's rival for the Democratic nomination, Hillary Clinton.