After landing in Tel Aviv, Mr Obama also referred to the stalled Israeli-Palestinian peace process, saying "peace must come to the Holy Land".
US officials have tried to lower expectations of any significant headway on restarting the peace process.
Syria, and Iran's nuclear ambitions are expected to loom large in talks.
Correspondents say Israelis are more preoccupied with instability in the wider Middle East region than with breathing new life into the peace process, which broke down in 2010 amid a dispute over continued Israeli settlement construction.
The leaders fell over themselves to be nice. Which is after all the purpose of this trip. To rebuild bridges, re-establish relationships.”
Settlement supporters are a big force in Israel's new coalition government.'Fundamental security interests'
Mr Obama was welcomed at Ben Gurion airport by Israeli Prime Minister Benjamin Netanyahu and President Shimon Peres.
He was introduced to Israeli ministers and leaders of religious communities and later shown a missile battery that forms part of Israel's Iron Dome defence system against rocket attacks.
"Even as we are clear eyed about the difficulties, we will never lose sight of the vision of an Israel at peace with its neighbours," he said in brief comments.
Barack Obama in Middle East
Wednesday: Meets Benjamin Netanyahu
Thursday: Meets Mahmoud Abbas
Friday: Visits Bethlehem's Church of Nativity and later departs for Jordan
He added: "The United States stands with Israel because it is in our fundamental security interests to stand with Israel. Our alliance is eternal. It is forever."
Mr Netanyahu said: "Thank you for unequivocally affirming Israel's sovereign right to defend itself by itself against any threat."
Mr Obama later visited Mr Peres at his official residence, from where he will go on to hold talks with Mr Netanyahu. On Thursday, he will visit the West Bank to meet Palestinian President Mahmoud Abbas.
At home Mr Obama has been criticised for not having visited Israel in his first term as president, with some saying it shows he is not close enough to the country.
The state of the economy and social issues dominated Israel's last election, and the president has said he is not going to the region bearing any grand peace plan.
The streets of Jerusalem are decorated with bunting and hundreds of US flags. Posters carry the official logo for this visit showing an American and Israeli flag fused together with the legend "unbreakable alliance".
Yet away from the official hype there is not great excitement among Israelis. The immediate concern of many is the increased security across the city. "There are cops all around. Traffic is going to be a nightmare. Many roads are closed already," one man remarked.
Today's Israeli newspapers look to Mr Obama for reassurance that he can prevent a nuclear-armed Iran. Maariv claims he has "only one to two weeks" to decide "whether to clash with Iran or allow the Iranians to laugh all the way to the atom bomb". Commentary in Yedioth Ahronoth says the president views "'the two-state model' as the only viable and realistic model" for peace with the Palestinians and will say so in lengthy talks with Israeli officials.
But with warnings that time is running out for a two-state solution, some still think he will try to lay the ground for some greater effort to restart talks, BBC North America editor Mark Mardell reports from Jerusalem.
The president's relationship with Mr Netanyahu has been notoriously frosty and one recent opinion poll suggested a mere 10% of the Israeli public had a favourable opinion of the US president.'Slap in the face'
The main event of this trip is a speech to the Israeli people - his main task is to build bridges and improve his image, which could give him more leverage over the new Israeli government, our correspondent adds.
Thousands of Israeli and Palestinian security officers have been assembled in Jerusalem and the Palestinians' de facto capital in the West Bank city of Ramallah, ahead of his trip.
Both Israeli and Palestinian groups have staged protests in the run-up to Mr Obama's visit.
In the West Bank city of Hebron, protesters wearing masks of Mr Obama and civil rights leader Martin Luther King called for an end to "apartheid".
There were clashes between the pro-Palestinian protesters and some of the settlers living in the divided city, and a number of Palestinians were arrested.
In Gaza City, protesters burned US flags outside UN offices, the Associated Press reports.
One protester said the visit would "only bring us shame and add more humiliation on to us", Reuters reports.
Hamas spokesman Sami Abu Zuhri said the visit was "ominous" and unwelcome, and that its consequences would be negative.
"It gives legitimacy to the occupation and confirms the political support of the United States [to Israel]," AP quoted him as saying.Meanwhile, Israelis have been staging protests in Jerusalem demanding Mr Obama free Jonathan Pollard, imprisoned in the US in 1987 for spying for Israel.eternal' alliance
