David Axelrod said Obama, who is vacationing in Hawaii, continues to closely monitor global events, including the situation in Gaza.
Obama had an intelligence briefing Sunday and plans to talk with his incoming national security adviser, Gen. James Jones, and Sen. Hillary Rodham Clinton, his nominee for secretary of state, Axelrod said.
Axelrod said Obama appreciates the information the Bush administration is sharing with him but added that comment from him was not appropriate.
"President Bush speaks for the United States until Jan. 20 and we're going to honor that," Axelrod said Sunday.
Axelrod refused to offer an opinion on the fighting between Israeli Defense Forces and Hamas militants.
"As Hamas began its shelling, Israel responded," Axelrod said on CBS' "Face the Nation."
Axelrod, a top presidential campaign official who is moving into Obama's White House inner circle, acknowledged that the United States has had a "special relationship" with Israel, calling it an "important bond, an important relationship."
Obama is "going to work closely with the Israelis. They're a great ally of ours, the most important ally in the region," Axelrod said. "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."
Hamas terrorists have been firing dozens of rockets and mortars into Israel since it decided earlier this month to abandon a months-long ceasefire with Israel. On Sunday, two rockets struck close to the largest city in southern Israel, Ashdod, some 23 miles from Gaza, reaching deeper into Israel than ever before.
In response to the return to fighting, Israel continued a second day of airstrikes into Gaza. So far, nearly 300 people, a large majority of them Hamas militants, have been killed there.
Arab nations around the region have condemned the Israeli action. Israeli Foreign Minister Tzipi Livni said her country has no plans to reoccupy Gaza, but would not discuss a possible ground offensive.
Rice issued a statement on Saturday condemning "the repeated rocket and mortar attacks against Israel and holds Hamas responsible for breaking the ceasefire and for the renewal of violence in Gaza." She also said the U.S. "calls on all concerned to address the urgent humanitarian needs of the innocent people of Gaza."
National Security Adviser Stephen Hadley said President Bush received an update on the situation on Sunday morning and is being notified as events change. He is expected to receive another intelligence update on Monday morning.
To that end, Secretary of State-designate Hillary Clinton has also been staying informed on the situation. As first lady, Clinton visited Gaza in 1998. Since becoming a New York senator, she has demonstrated firm support for Israel.
Clinton's viewpoint is unlikely to differ much from Obama's.
"The president-elect was in Sderot last July, in southern Israel, a town that's taken the brunt of the Hamas attacks. And he said then that, when bombs are raining down on your citizens, there is an urge to respond and act and try and put an end to that," Axelrod said.
But, he added, the president-elect wants to manage Mideast relations "in a way that will promote the cause of peace, and work closely with the Israelis and the Palestinians on that -- toward that objective."
Republican Tennessee Sen. Bob Corker, a member of the Senate Foreign Relations Committee, said he is concerned about the conflict, including the largest number of casualties in two decades, but even the Palestinian government led by Mahmoud Abbas has condemned Hamas.
"Our hearts and prayers go out to people on both sides, and certainly especially the civilians who have been harmed in the Gaza area. But mostly, it's been confined to people who are part of the security forces for Hamas, and certainly all of us want to see an end to this conflict and some long-term peace settlement actually occur there."
Democratic Ohio Sen. Sherrod Brown advised against Israel calling up reservists.
I'm not sure it's a good idea. I mean, Israel certainly has the right to self-defense, of course. Hamas has not recognized Israel's right to exist. ... But I'm hopeful that with a new president -- you know, you look at President Bush is now in a petty weakened state, and countries around the world know that. I'm hopeful that as this transition comes, as we look to January, that strong presidential leadership can make a difference here," Brown said, appearing on ABC's "This Week" with Corker.