Israel captured those territories in the 1967 Six Day War.
“We expect huge pressure and hard days, but we will not go to negotiations like blind people,” Abbas was quoted as telling Fatah leaders.
Abbas’ comments were published on Wednesday in a Palestinian daily, and confirmed by his adviser Sabri Saidam, who was present at the meeting.
The Palestinian leader said Obama’s assurances concerning the negotiations were delivered last week by US Middle East envoy George Mitchell.
No direct talks
Israeli Prime Minister Benjamin Netanyahu says he wants to move to direct talks immediately, but refuses to agree to a framework for the negotiations.
Palestinians are reluctant to engage with Netanyahu, who has retreated from some of the positions of his predecessors.
Fighting broke out in the West Bank on Wednesday between Palestinians and Israeli soldiers who bulldozed two homes and several shacks that Israel said were built illegally.
Residents shoved and punched soldiers who hurled tear gas and stun grenades to drive them back. Palestinians rarely receive permits to build in areas ruled by Israel’s military.
Foreign Ministry Spokesman Yigal Palmor, meanwhile, said South Africa’s ambassador has returned to Israel, weeks after he was withdrawn by his government over a raid by Israeli navy commandos on a Gaza-bound flotilla in which nine activists were killed.
The raid unleashed a wave of international criticism against Israel, particularly for its blockade of the Hamas-ruled Gaza Strip. Palmor said the South African envoy returned Monday.
In a separate development, the Israeli military has submitted a new report to the United Nations on its three-week offensive in Gaza in the winter of 2008-2009.
It said it would take greater precautions to avoid civilian casualties, but reiterated that it considered the offensive a necessary and proportionate response to years of Hamas rocket attacks on Israeli towns.
Some 1,400 Gazans were killed in the war, including hundreds of civilians. Thirteen Israelis were also killed.
UN investigators wrote in a report last year that they found evidence that both sides committed war crimes.
Hamas was cited for indiscriminate rocket fire on Israeli civilians, while Israel was accused of using disproportionate force and intentionally harming civilians.