"If it was up to me, I'd let them come," Trump said on a tarmac in Los Angeles. "I would certainly not want to keep people out if they want to come."
The administration is required to issue the visas under the U.N. agreement with the United States, the host country of the organization. The State Department, which issues visas, does not comment on individual cases.
U.N. Secretary General Antonio Guterres told reporters Wednesday that it has been in contact with the U.S. in order to solve all delegations' outstanding visa problems.
Saudi Arabia alleged Wednesday that the attack by drones and cruise missiles on the heart of the kingdom's oil industry was "unquestionably sponsored by Iran," but did not directly accuse Tehran of launching the assault. Iran, which has denied being involved, said it will retaliate "immediately" if it is targeted in response.
Iran's state-run news agency IRNA said earlier that Iranian President Hassan Rouhani and his foreign minister, Mohammad Javad Zarif, may not attend the general assembly in New York because the U.S. had not yet issued them visas. IRNA said Zarif was to travel there Friday and Rouhani was to follow Monday.
The U.N. has been floated as a possible place for a meeting between Trump and Rouhani, but U.S. officials and Iran's Supreme Leader Ayatollah Ali Khamenei have said direct talks are not planned.