"He said then that when bombs are raining down on your citizens there is an urge to respond and act to put an end to that," Axelrod told CBS talkshow Face the Nation on Sunday.
"That's what he said then, and that’s what he believes."
He said Obama planned to work closely with Israel which he said was Washington's "most important ally in the region".
|Critics say US support for Israel
could backfire [Reuters]
"They're a great ally of ours... And that is a fundamental principle from which he'll work. But he will do so in a way that will promote the cause of peace, and work closely with the Israelis and the Palestinians on that."
Like Bush, Obama has ruled out talks with Hamas for its refusal to recognise Israel.
During his White House campaign, Obama pledged to further cement the US-Israeli alliance saying he would "always stand up for Israel's right to defend itself in the United Nations and around the world".
Even so, critics of US Middle East policy say Obama ought to express more empathy for the Palestinians' situation.
Michael Hudson, professor of international relations at Georgetown University said that by backing Israel's position the US was opening itself up to attack.
"If you're identified with an Israel that is bombing indiscriminately and disproportionately, this is really good for Osama Bin laden, it's good for extremists all across the region and I fear that Americans as well as Israelis will now suffer," he told Al Jazeera.
In contrast to the incumbent president, Obama has pledged to take an active personal role in peace efforts early in his administration.
How long those efforts are waylaid by the ongoing fighting, however, is a question no one can yet answer.