Trump, a Republican who promised a far-reaching immigration crackdown, suspended refugee resettlement after he took office in January.
In April, Trump's administration terminated temporary deportation protections for thousands of Afghans in the US.
"I will try to save them, starting right now," Trump said in a post on Truth Social that linked to an article on the Afghans held in limbo there.
Trump cited news website Just the News as saying that UAE officials were preparing to hand over some Afghan refugees to the Taliban.
Reuters has not confirmed the report.
The UAE, a close security partner of the United States, agreed in 2021 to temporarily house several thousand Afghans relocated from Kabul as the Taliban ousted the US-backed government during the final stages of the US-led withdrawal.
Nearly 200,000 Afghans were brought to the US by former president Joe Biden's administration since the chaotic US troop withdrawal from Kabul.
Canada agreed in 2022 to resettle about 1000 of the Afghans still held in the UAE after a US request.
It is unclear how many remain in the Gulf country.
Some countries have forced Afghan refugees to return to Afghanistan.
Nearly two million Afghans were returned from Iran and Pakistan in the past seven months, the United Nations said last week.
Germany on Friday deported 81 Afghan men to Afghanistan amid a tightening of refugee admissions.
Some other European Union countries are pushing to tighten asylum rules in the bloc.
In the United States, Democrats have urged Trump to restore temporary protected status for Afghans, saying women and children could face particular harm under the Taliban-led government in place since 2021.
Refugees include children cleared to reunite with their parents, relatives of Afghans already admitted and tens of thousands of Afghans who worked for the US government during the 20-year war.
Shawn VanDiver, president of the #AfghanEvac advocacy group, urged Trump to follow up on his post with action.
"President Trump has the authority to do the right thing. He should instruct DHS (Department of Homeland Security) and the Department of State to expedite processing, push for third-country partnerships, and ensure that we never again leave our wartime allies behind," he said in a statement.
