Advocates had been imploring Australian officials to meet with the team to secure their safety after the squad were seen making what appeared to be an "SOS" hand signal on Sunday night after their final Asian Cup match.
The team is staying at the Royal Pines resort on the Gold Coast and is due to leave Australia later this week.
"Australia is making a terrible humanitarian mistake by allowing the Iran National Woman's Soccer team to be forced back to Iran, where they will most likely be killed," Mr Trump said in a post on Truth Social about 1am AEDT.
"Don't do it, Mr. Prime Minister, give ASYLUM. The U.S. will take them if you won't," he said.
Mr Trump later posted another message saying he had spoken with Mr Albanese and praised the prime minister for his handling of a "rather delicate situation".
"Five have already been taken care of, and the rest are on their way," Mr Trump said, referring to the Iranian players.
"Some, however, feel they must go back because they are worried about the safety of their families, including threats to those family members if they don't return."
Rana Dadpour, the founder of women's rights group AUSIRAN, on Monday urged Australian officials to organise private meetings with the team members before they leave the country, warning they could face execution if they return home.
"We need to talk with these girls away from the handlers and the regime-affiliated people who are following them right now in Australia," she told AAP.
"If they want to stay, I think we need to provide them with every support that we can."
Leaving their final match of the competition on Sunday night, at least one of the women appeared to make the international signal for help through the window of the team bus - raising an open palm, crossing the thumb over it and folding the four fingers over the top.
Protesters surrounded the bus and the women appeared to film the crowd through the window.
Media reports on Monday night suggested several members of the team had evaded their handlers and were under police protection in Queensland.
"The government should immediately revoke the visas of any accompanying security personnel involved in threats or intimidation against these brave women, and put them in immigration detention now," Liberal MP Julian Leeser said on Monday evening.
"Every member of the Iranian Women's Football Team should have an opportunity to speak individually with an Australian Border Force agent or other government official, and to seek asylum if they want it," Mr Leeser said.
The opposition frontbencher said "we should offer the women of the Iranian team an alternative to returning to Iran".
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