Obama repeated U.S. warnings to the Syrian government to keep chemical weapons off the battlefield or out of the hands of groups such as Hezbollah.
He said he has ordered an investigation into whether the Syrian government used chemical weapons against its own people, adding he was "deeply skeptical" of any claim the opposition had done it.
"Once we have established the facts, I have made clear that the use of chemical weapons is a game-changer," Obama declared, stopping short of saying what he would do if Syria had crossed his "red line" for stronger action.
Critics, including Republican opponents, say Obama has failed to show necessary global leadership by providing military aid to the Syrian opposition or offering help like establishing a "no-fly" zone over Syria similar to NATO steps taken in Libya during the Arab Spring uprising.
Earlier, Netanyahu and Israeli President Shimon Peres greeted Obama at an arrival ceremony in Tel Aviv, where Obama said his visit was " an opportunity to reaffirm the unbreakable bond between our nations, to restate America's unwavering commitment to Israel's security, and to speak directly to Israel and to your neighbors."
In a quip to Netanyahu, Obama said, "It is nice to get away from Congress," reflecting the chronic political infighting in Washington.
Obama's first stop Wednesday was at an Iron Dome missile defense launcher in Tel Aviv.
Designed by Israel and funded by the United States, the battery was deployed at the height of November's fighting between Israel and Hamas. It intercepted a rocket headed for Tel Aviv, Israeli ambassador to the United States Michael Oren said.
Afterward, the president went to Jerusalem to meet separately with Peres and Netanyahu.
A shaky relationship
Obama's relationship with Netanyahu has never been warm, and the Israeli prime minister supported Republican challenger Mitt Romney -- a former business colleague -- in last year's presidential election.
In his first term, Obama got off to a rocky start with Netanyahu by pushing for a freeze on Israeli settlements, but his vocal support for the Israeli prime minister through the November crisis with Hamas and U.S. financial support for the Iron Dome anti-missile program could pave the road for greater trust in the relationship.
White House officials said Obama was not bringing a new peace initiative and lacked optimism that enough solid ground existed to try to revive direct negotiations between Israel and the Palestinians over the declared goal of both sides for separate, neighboring states.
Most of all, the president's aides said, Obama wanted to assess how prepared -- if at all -- Netanyahu and Palestinian leader Mahmoud Abbas were to return to negotiations.
Palestinians want Obama to prove there were consequences for Israel's continued construction of new settlements in what they consider to be disputed areas.
Their grievances are evident in more personal ways: Posters on Ramallah streets sarcastically advise Obama not to bring his smartphone because Israel does not allow 3G or better service in the Palestinian territories.
Before meeting Peres on Wednesday, Obama and the Israeli president planted a magnolia tree descended from those at the White House to symbolize the deep roots of the relationship between their nations, the White House said.
The two leaders also were serenaded with the song "Tomorrow" by three young Israelis who dedicated it "from all the children who dream of peace."