Barack Obama said Wednesday that he brings an "unshakable commitment" to Israel's security, but called on the nation to make peace with the Palestinians and warned of the "grave threat" posed by a nuclear Iran.

Obama spoke at a press conference in Sderot, Israel, near the Gaza border, after meeting with several high-ranking Israeli officials, including President Shimon Peres. The city has been a frequent target of rocket attacks from Hamas terror operatives in Gaza.

Shards of rockets were in stacks behind Obama as a reminder of ongoing attacks.

"I bring to Sderot an unshakable commitment to Israel's security," Obama said, stressing that America "must always" stand up for Israel's right to defend itself. "The state of Israel faces determined enemies who seek its destruction. But it also has a friend and ally in the United States that will always stand by the people of Israel."

Though Obama told the American Israel Public Affairs Committee in June that he supports an undivided Jerusalem, the Illinois senator said Wednesday that while Jerusalem "will be the capital of Israel," it is up to the Palestinians and Israelis to decide if the capital will also be shared with a Palestinian state. He denied changing his position.

Obama said it is "strongly in the interest of Israel's security to arrive at a lasting peace with the Palestinian people," but previewed a much more engaged role in dealing with Iran.

"I will take no options off the table in dealing with this potential Iranian threat," Obama said. "You would have countries in the Middle East who see the potential need to obtain nuclear weapons -- any of these countries including Iran who have ties to terrorist organizations, which means that some day you could have loose nuclear materials falling into the hands of terrorists.

"That is our single most important threat to Israel but also to the United States of America," he said.

Obama defended his proposal to negotiate with Iran and said he would use "big sticks and big carrots" to persuade the country's leaders not to develop nuclear weapons.

"My whole goal in terms of having tough, serious direct diplomacy is not because I'm naive about the nature of any of these regimes. I'm not," Obama said at a press conference. "It is because if we show ourselves willing to talk and to offer carrots and sticks in order to deal with these pressing problems, and if Iran then rejects any overtures of that sort, it puts us in a stronger position to mobilize the international community to ratchet up the pressure on Iran."

The campaign of Republican presidential candidate John McCain quickly responded that Obama was backtracking on his expressed willingness to meet with Iran's leaders without preconditions.

A year ago, Obama was asked whether he would meet personally, without preconditions, with leaders of Iran and other hostile nations during the first year of his administration to resolve differences with the United States. Obama responded at the time: "I would."

On Wednesday Obama said, "I think that what I said in response was that I would at my time and choosing be willing to meet with any leader if I thought it would promote the national security interests of the United States of America. And that continues to be my position. That if I think that I can get a deal that is going to advance our cause, then I would consider that opportunity. But what I also said was that there is a difference between meeting without preconditions and meeting without preparation."

Later during a meeting with Israeli Prime Minister Ehud Olmert, Obama reiterated his "stalwart support" for the country's security.

Olmert said "the situation in Iran is of course the main concern for the people of Israel."

Obama tried to use Wednesday's event to allay doubts about his support for Israel. Many Israelis are worried by Obama's willingness to talk to Tehran, a bitter enemy of the Jewish state. Many U.S. Jewish voters supported Obama's rival Hillary Rodham Clinton for the Democratic presidential nomination, and some have questioned his commitment to Israel.

Earlier in the West Bank town of Ramallah, Obama assured Palestinian leaders he'd get involved in the Mideast conflict quickly, a top Palestinian official said.

In his meeting with Palestinian President Mahmoud Abbas, Obama confirmed "that he will be a constructive partner in the peace process" and would not "waste a minute" if elected, Abbas aide Saeb Erekat said.

Obama foreign policy adviser Susan Rice said the Secret Service was in charge of security, but did not deny that local agencies might help, such as the Fatah-run government in the West Bank or even Hamas.

The Islamic militant Hamas group, which rules the Gaza Strip, said Obama was not welcome and criticized Abbas, a bitter rival, for receiving him. "Obama wants to go to the White House through Tel Aviv, at the expense of the Palestinians," said Fawzi Barhoum, a Hamas spokesman.

Obama also met with Israeli Defense Minister Ehud Barak and parliamentary opposition leader Benjamin Netanyahu, whose Likud Party takes a hard line against the Palestinians.

Obama met with Barak and Netanyahu at Jerusalem's posh King David Hotel, where an "Israel for Obama" campaign poster was draped over an armchair in the lobby. The poster included Obama's campaign slogan -- "Change you can believe in" -- in Hebrew.

And in an apparent show of friendship Wednesday, the mayor of Sderot gave Obama a T-shirt at the end of the press conference. Also showing it to the pool of reporters, the shirt read "I [heart] Sderot." Piercing the center of the heart appeared to be a missile.

FOX News' Bonney Kapp and The Associated Press contributed to this report.