"What are you willing to do for peace? What hard steps are you willing to take?" Obama told leaders of diverse Jewish organizations he planned to ask Israelis.
He met with about 25 U.S. Jewish leaders at the White House for an hour Thursday in a meeting that was not on his public schedule.
Several participants spoke with a few news organizations afterward, largely keeping their comments general, as the White House requested.
Obama told the group he did not plan to lay out a "grand" U.S. peace plan during the visit, attendees told the Los Angeles Times and the Jewish Telegraphic Agency.
Indeed, Obama said he thought prospects for peace were "bleak" right now, two attendees told JTA.
But "that doesn't mean six or nine or 12 months from now we won't be in the midst of a policy initiative," he said.
Obama said he does plan to counsel Israeli and Palestinian leaders against making "unilateral" moves, attendees told JTA.
He didn't elaborate, but administration references to unilateral moves generally refer to Israeli West Bank settlement activity and Palestinian attempts to achieve statehood recognition.
The White House has not announced the dates for Obama's trip, but Israeli news media have said he will arrive March 20.
He plans to meet with Israeli Prime Minister Binyamin Netanyahu, who is still working to cobble together a government after January's election. Obama also plans to meet with Palestinian Authority President Mahmoud Abbas in the West Bank city of Ramallah and with King Abdullah II in Jordan.
The primary goal of the Israeli leg of the trip is to demonstrate Washington's "unshakable support" for Israel, Obama said.
When he talks with Israeli leaders, Obama told the group he intends to discuss growing security threats Israel faces from Iran, Syria, Egypt and other parts of the Middle East.
When members of the group urged him to step up U.S. threats against Iran to persuade it to accept limits on its disputed nuclear program, Obama demurred.
"I'm not going to do extra chest-beating just so people think I'm tough," the Los Angeles Times quoted him as saying.
Obama said loud threats could backfire by closing off any remaining chance of a diplomatic solution.
He quoted a Chinese proverb attributed to ancient Chinese military general and philosopher Sun Tzu.
The proverb says, "Build your opponent a golden bridge to retreat across."