Obama was to meet Palestinian President Mahmud Abbas at 9am and then Prime Minister Salam Fayyad, on the second day of his visit to Israel, the West Bank and Jordan, which is dominated by challenges posed by Iran and Syria.
Hours before Obama was to board his helicopter to fly to Ramallah to meet the Palestinian leadership, two rockets fired by militants in the Hamas-run Gaza Strip hit southern Israel.
In only the second such attack since November, the rockets crashed down in Sderot, a border town often targeted by rockets, which Obama visited in a previous visit to Israel while a presidential candidate in 2008.
Obama, on the first foreign trip of his second term, says he has came to the Holy Land simply "to listen" to the parties about how to resume peace talks which have been frozen for two-and-a-half years.
He said he decided against coming armed with a comprehensive peace plan that might not be fit for current political conditions.
"Ultimately, this is a really hard problem," Obama said during a news conference with Israeli Prime Minister Benjamin Netanyahu on Wednesday.
"It's been lingering for over six decades. And the parties involved have, you know, some profound interests that you can't spin, you can't smooth over. And it is a hard slog to work through all of these issues."
Obama's new approach was a stark contrast to early in his first term, when he declared Israeli settlement building to be illegitimate and promised to dedicate himself to peace.
He admitted on Wednesday that he had perhaps made mistakes, but argued that he was not the only US leader to have come a cropper on the issue.
"I hope I'm a better president now than when I first came into office," Obama said.
"I'm absolutely sure that there are a host of things that I could have done that would have been more deft and, you know, would have created better optics."
Palestinian peace negotiator Nabil Shaath on Wednesday published an op-ed message in the Israeli newspaper Haaretz, urging Obama to prove his commitment to a two-state solution by turning pledges into deeds.
"We could have saved lives and political capital if President Obama had shown the determination to create the right environment for meaningful decisions leading to a two-state solution," he wrote.
"Now, rather than calling for the resumption of a meaningless 'peace process', we Palestinians expect real action on the ground."
Shaath said Obama had disappointed Palestinians who once warmed to his calls for an end to settlement building.
"President Obama appeared to give up on his goal," he said.
Separately on Wednesday, Palestinian activists set up a protest camp on a strip of West Bank land east of Jerusalem where Israel has announced controversial plans to build, demanding an end to Obama's "bias and support for Israel."
Israel's plan to build thousands of new settler homes in an area called E1 has sparked a major international backlash, with experts saying it could wipe out hopes for the establishment of a viable Palestinian state.
Netanyahu, however, on Wednesday re-committed to the notion of a two-state solution for the first time since he was re-elected in January, albeit in a weaker political position.
"Let me be clear: Israel remains fully committed to peace and to the solution of two states for two peoples," he said, standing beside Obama.
The Palestinians are hoping Obama will help broker the release of more than 1,000 prisoners held by Israel and also free up $700 million in blocked US aid.
At Wednesday's news conference, Obama accepted the Jewish state would not cede its right to confront Iran's nuclear threat to the United States.
"I would not expect that the prime minister would make a decision about his country's security and defer that to any other country," he said.
Washington has worried that Netanyahu's hawkish rhetoric on Iran and warnings Tehran could get most of the way to a nuclear bomb within months - a shorter timeline than Washington's - have sparked fears of an Israeli strike.
But Obama came to Israel apparently determined to remove all doubt about his commitment to Israel which have harmed his reputation here, and proven a thorny political issue at home.
He will return from the West Bank later on Thursday to redouble his Israeli charm offensive by giving a speech to hundreds of young people at a conference centre in Jerusalem.