A spokesman for the coalition denied that a major ground force has landed, refusing to comment on “ongoing operations”.
But Yemeni government and militia forces said several dozen troops had landed in the main southern city, with some sources saying they were to assist in fighting for its international airport.
A journalist saw several men in the vicinity of the airport dressed in military-style clothing, wearing helmets and carrying sophisticated weaponry.
“A limited coalition force entered Aden and another force is on its way”, a Yemeni government official in Aden said.
A leading member of the so-called “popular committees” supporting exiled President Abd-Rabbu Mansour Hadi said the newly deployed troops “will start helping us in fighting the Houthis and (former president Ali Abdullah) Saleh’s forces”.
The troops would mainly back pro-Hadi fighters around the rebel-held airport, which has changed hands several times and was again the focus of heavy fighting on Saturday night, he said.
Other militia commanders confirmed that a few dozen coalition soldiers, mostly Saudis and Emiratis of Yemeni origin, were on the ground in Aden.
One militia source said some 30 soldiers from coalition countries had been deployed to “supervise” operations to retake the airport.
Coalition spokesman Brigadier General Ahmed Assiri denied a major ground force had landed in Aden. “I can assure you that no (coalition) forces disembarked on the ground in Aden today,” he told Saudi news agency Al-Ekhbariya.
But in comments to Doha-based Al-Jazeera television, he said that “all options are open”.
“The coalition leadership will not spare any effort to support the resistance and achieve positive results on the ground,” Brig Gen Assiri said.
On Sunday, coalition warplanes pounded rebel positions in and around the airport as clashes raged on, said a pro-Hadi military official.
Doctors in Aden said that at least 18 people, most of them civilians, were killed since Saturday and 65 others wounded.
Local officials said most of the casualties resulted from rebel mortar shelling and gunfire across residential areas.
Human Rights Watch on Sunday accused the coalition of using US-supplied cluster bombs in its operation, warning of the long-term danger to civilians.
HRW said it had gathered photographs, video and other evidence indicating that cluster munitions had been used in air strikes against the Houthi rebel stronghold of Saada province in Yemen’s northern mountains in recent weeks.
Cluster munitions are prohibited by a 2008 treaty adopted by 116 countries, but not by Saudi Arabia and its coalition partners or the United States.
“Saudi-led cluster munition air strikes have been hitting areas near villages, putting local people in danger,” said HRW arms director Steve Goose.
Saudi Arabia denied it was using cluster munitions earlier in the campaign.
Moroccan King Mohammed VI visited Saudi Arabia on Sunday and discussed “regional and international developments” with King Salman, the official SPA news agency reported.