In a series of meetings and calls since March, including before Mr. Biden announced the U.S. withdrawal, lawmakers and resettlement officials warned the White House and the State Department that the situation required an urgent response — one that could not be addressed by the special visa program, which took too much time, according to resettlement and former government officials who spoke on the condition of anonymity to describe internal discussions.

The special visa program requires applicants to clear extensive levels of vetting and provide evidence of their work — documents that can be hard to obtain for families who have been forced to flee their homes. The Biden administration has blamed the previous administration for exacerbating the delays through “extreme vetting” requirements.

The calls for swift evacuations picked up even as the Biden administration deployed additional staff members in Washington and at the embassy in Kabul to address the backlogs. One official said the administration cut through the bureaucracy by slashing in half processing delays that totaled an average of two years when Mr. Biden came into office, lobbying Congress to expand the number of visas and waiving requirements for medical examinations.