But peace, Abbas said, will not come "through violence, occupation, walls, settlements, arrests, siege and denial of refugee rights."
In his speech in Jerusalem, the president also issued a strong warning to the players who threaten progress toward reaching stability in Israel and the Middle East.
Drawing large applause from the crowd, Obama stressed that "every country that values justice should call Hezbollah what it truly is, a terrorist organization," and he reissued his warning to Syria about the use of chemical weapons.
"I have made it clear to Bashar al-Assad and all who follow his orders: We will not tolerate the use of chemical weapons against the Syrian people or the transfer of those weapons to terrorists. The world is watching, and we will hold you accountable," the president said.
On Iran, the president cautioned the country against obtaining and using nuclear weapons and repeated his willingness to consider all options to ensure nuclear weapons are not in the hands of the Iranian government.
"Because of the cooperation between our governments, we know that there remains time to pursue a diplomatic resolution," he said.
"But Iran must know this time is not unlimited. And I have made the position of the United States of America clear: Iran must not get a nuclear weapon. This is not a danger that can be contained."
Obama was interrupted by hecklers once during the speech, a moment he brushed off as a familiar reminder of speeches in the United States.
"This is part of the lively debate that we talked about," he said. "I have to say we actually arranged for that because it made me feel at home. I wouldn't feel comfortable if I didn't have at least one heckler."
The president met Wednesday with Israeli Prime Minister Benjamin Netanyahu, with whom the president has had a rocky relationship.
"I know that in Israel's vibrant democracy, every word and gesture is carefully scrutinized. But I want to clear something up just so you know.
"Any drama between me and my friend Bibi [Netanyahu] over the years was just a plot to create material for Eretz Nehederet," Obama said today in reference to a satirical Israeli television show. "We just wanted to make sure the writers had good material."