The federal government has committed to providing 3000 such visas this financial year alongside additional evacuation flights.
It comes after a RAAF C-130 Hercules evacuated 26 people from Kabul airport to the United Arab Emirates, where the Australian military is based for the operation.
Immigration Minister Alex Hawke says more flights are planned, but stressed the complexity of the situation on the ground.
"That first mission was an absolute success," he told ABC radio on Thursday.
"It is very hard to get to the airport. It is very hard to get through in a controlled way to a plane, and we're able to get out Australian citizens, Afghan nationals that we have an obligation to."
The government previously conceded it was unlikely all Afghans who helped Australia would be able to be rescued.
Its provision of 3000 humanitarian visas is part of its existing intake, rather than a special allocation, and is below other nations' commitments.
"That is what we assess as the amount of people that we will be able to take safely. That number will increase," Mr Hawke said.
World Vision is among groups calling on Australia to create an additional 20,000 humanitarian visas for people fleeing Afghanistan.
More than 300 organisations have signed an open letter saying the government has a moral duty to the Afghan people.
"After almost two decades of intervention and promises to the Afghan people, promises of protection for persecuted groups, women, democratic freedoms and rule of law, Prime Minister Scott Morrison has a moral obligation to act in response to the humanitarian crisis in Afghanistan," the letter said.
Meanwhile, the government has promised not to return Afghans living in Australia on temporary visas for now.
It is refusing the offer of permanent residency to Afghans who arrived by boat.
"We've made it very clear there'll be no change, now, in the status of people who came by boat," Mr Hawke said.
Since April, 430 Afghans who helped allied forces during the two-decade war and their families have been brought to Australia.
Labor MP Anne Aly said her party had been calling for years for greater generosity towards Afghans seeking to leave the country.
"I hold such grave fears for the people in Afghanistan, particularly the women and the children, particularly the ethnic minorities there," she said.
"Everything that we can possibly do we need to be throwing at this."
Defence Minister Peter Dutton said some visa applications would take time because of the complexity of identity and other checks.
He said he was aware of some Afghans who had worked with Australian officials and switched their allegiance to the Taliban.