Biden, seated beside Ghani and Abdullah in the Oval Office, called them "two old friends" and said U.S. support for Afghanistan was not ending but would be sustained despite the U.S. pullout, Reuters reported.
"Afghans are going to have to decide their future, what they want," said Biden, saying the "senseless violence has to stop."
Ghani said Afghan security forces had retaken six districts on Friday. He said he respected Biden's decision and that the partnership between the United States and Afghanistan is entering a new phase.
Speaking with reporters after the meeting, Ghani said the United States' decision to withdraw troops was a sovereign one and it was Kabul's job to "manage consequences."
He added that Biden had clearly articulated that the U.S. embassy would continue to operate and security aid would continue and in some cases move on an accelerated schedule.
Abdullah said in a Reuters interview after the Biden meeting that stalled intra-Afghan talks on a political settlement to decades of strife should not be abandoned unless the insurgents themselves pull out.
The Oval Office meeting could be as valuable to Ghani for its symbolism as for any new U.S. help because it will be seen as affirming Biden's support for the beleaguered Afghan leader as he confronts Taliban gains, bombings and assassinations, a surge in COVID-19 cases and political infighting in Kabul.
Biden's embrace, however, comes only months after U.S. officials were pressuring Ghani to step aside for a transitional government under a draft political accord that they floated in a failed gambit to break a stalemate in peace talks.
Biden has asked Congress to approve $3.3 billion in security assistance for Afghanistan next year and is sending 3 million doses of vaccines there to help it battle COVID-19.
U.S. officials have been clear that Biden will not halt the American pullout – likely to be completed in the coming weeks -and he is unlikely to approve any U.S. military support to Kabul to halt the Taliban's advances beyond advice, intelligence, and aircraft maintenance.
Earlier, the Afghan leaders met for a second day on Capitol Hill, where Biden's withdrawal decision met objections from many members of both parties.