U.S. President Barack Obama visits the West Bank on Thursday, where he will hold talks with Palestinian President Mahmoud Abbas and Prime Minister Salam Fayyad.
Hours before the meeting with Mr. Abbas, Israeli police said militants in the Hamas-ruled Gaza Strip fired two rockets into southern Israel, damaging the yard of a house but causing no injuries.
Mr. Obama said Wednesday after arriving for his first visit to Israel as president that he wants to speak directly to the Israeli people and their neighbors about his belief that "peace must come to the holy land."
Many Palestinians have expressed disappointment with Mr. Obama, and scattered protests formed in Palestinian territories before he arrived in the region Wednesday.
Mr. Obama met with Israeli Prime Minister Benjamin Netanyahu and President Shimon Peres, who said both the United States and Israel are trying to restart peace negotiations with the Palestinians.
"We have already agreed that the goal is a two-state-for-two-peoples solution. There is no better one, more achievable one. We consider that the president of the Palestinian Authority Abu Mazen is our partner in that effort to stop terror and bring peace."
Mr. Obama said he benefited from the Israeli president's views on how to deal with turmoil in the Arab world, the perceived "perils of a nuclear-armed Iran" and the "imperatives" of peace between Israelis and Palestinians.
"I reaffirmed to President Peres, as I will throughout my visit, that in this work, the state of Israel will have no greater friend than the United States. And the work we do in our time will make it more likely that the children we saw today, alongside children throughout the region, have the opportunity for security and peace and prosperity."
Mr. Obama said there is not much difference between U.S. and Israeli assessments of how close Iran is to potentially developing a nuclear weapon.
He said he would not expect Israel to defer any decisions about military action to another country - even a close ally such as the United States. He repeated the U.S. position that "all options" are on the table for stopping Iran from acquiring a nuclear weapon but said there is still time to resolve the issue diplomatically.
Israel sees an Iranian nuclear weapon as a threat to its existence due to Tehran's calls for the destruction of the Jewish state. Iran insists that its nuclear program is designed only for peaceful research and electricity generation.
Mr. Netanyahu said he and Mr. Obama have a "common assessment" that it will take Iran about one year to make a nuclear bomb if it decides to do so. He said Iran's continued enrichment of uranium, a key ingredient of such a bomb, is a separate matter.
The Israeli prime minister said he believes that if Iran "gets through" the enrichment process, it will reach an "immunity zone" - a reference to a situation in which military action would not be able to stop it. In a speech to the United Nations last September, Mr. Netanyahu warned that Iran could reach such a "red line" by the middle of this year.
It was not clear if Mr. Obama shared the Israeli leader's view of the "immunity zone."
On Friday, his schedule includes talks with King Abdullah in Jordan, where the United States has been helping authorities to cope with a flood of refugees from the Syrian civil war.
In addition to the meetings, Mr. Obama is scheduled to visit a set of cultural and religious sites in the region, including seeing the Dead Sea Scrolls at the Israel Museum and a stop at the Church of the Nativity in Bethlehem.