Mr. Lees-Galloway said that immigration officials would contact those who qualified for the new visas. Survivors of the attacks said Tuesday evening that they had not yet heard from the authorities and that word had spread through friends or on social media.

One of the survivors, Tofazzal Alam, 26, said that he had struggled to eat and sleep after the attack on the Linwood mosque, and that uncertainty over his visa had compounded the stress.

His permit to stay in the country is tied to his job as a door-to-door salesman — work that Mr. Alam, though he was not injured in the attack, said he was no longer able to do.

“I am a people person; I love to meet with different people,” said Mr. Alam, who has lived in New Zealand for five years and is married. “But now I feel afraid of strangers. I can only talk to people or meet people whom I know.”

Mr. Alam said permanent residence would allow him more freedom to seek an office job where he could encounter mostly the same people every day. He said he did not want to move back to his home country, Bangladesh.

“We have got so much love and respect for this country,” he said. “We have many things to give back.”

One of those shot in the attacks, Azmat Hussein, said the change was “very good news.”

Mr. Hussein, a welder who migrated with his family from Fiji on a work visa in 2016, had made an unsuccessful application for permanent residence shortly before the attacks. He had fallen just short on an English language test and was relieved that he would no longer need to meet the standard.