Abbas arrived at the White House two weeks after Israeli Prime Minister Benjamin Netanyahu, warning that time was running short for a final deal and saying Israel could show it was serious by honouring a scheduled release of Palestinian prisoners this month.
Obama, personally supporting Secretary of State John Kerry's exhaustive Middle East peace drive at a critical moment, is pressing both sides to accept a framework to carry negotiations past an end-of-April deadline.
"It is very hard, very challenging. We are going to have to take some tough political decisions and risks if we're able to move it forward."
Obama said that everyone understood the shape of an "elusive" peace agreement between Israel and the Palestinians, saying it would be based on 1967 lines with mutual land swaps.
Abbas sat beside Obama in the same Oval Office chair recently used by Netanyahu, when the Israeli leader complained Israel had done its part over decades of peace talks and the Palestinians hadn't done theirs.
"Time is not on our side, especially given the very difficult situation that the Middle East is experiencing and the entire region is facing."
Abbas did not use a photo opportunity before the talks to directly address the Israeli government's demand for the Palestinians to recognise Israel as a "Jewish" state in public.
But he did say through a translator that the Palestinians had recognised Israel's legitimacy in 1988 and in "1993 we recognised the state of Israel.
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