SANA'A, Yemen - Shiite rebel forces and their allies pushed into the heart of Yemen's second-largest city and seized the presidential palace Thursday, scoring another major advance and exposing the apparent limitations of Saudi-led airstrikes seeking to restore the country's president.

The loss of the southern port city of Aden to the rebel alliance would be a clear setback to the Saudi-run military campaign, which so far has focused on airstrikes as commanders assess whether to mount a potentially difficult and costly ground invasion.

A chief goal of the coalition's offensive is to carve out enough of a safe haven for the return of self-exiled President Abed Rabbo Mansour Hadi, who fled his last redoubt in Aden late last month and took refuge in Saudi Arabia.

But the rebel forces, which already control the capital, Sana'a, have managed to drive deeper into Aden with tanks and heavy armored vehicles, displaying the strength of their arsenal and demonstrating their ability to withstand the nearly round-the-clock aerial attacks that began last week.

It was unclear how long the resistance to the rebel advance could hold on.

Residents said pro-Hadi groups in the city, called Popular Committees, appeared to have largely disbanded or fell back during the fighting. The Shiite rebels, known as Houthis, and their allied fighters reached as far as the central Crater district, their deepest move into Aden, a key port and gateway to Yemen's south.

Ordinary citizens, armed with automatic weapons but heavily outgunned, then rushed into the battle in quickly formed ragtag militias, offering a guerrilla-style defense of the last major foothold of Hadi's government.

Holding Aden would earn the rebels another gain: a staging ground to try to control the islands of the Bab al-Mandab strait, one of the world's busiest shipping lanes, at the mouth of the Red Sea.

"For the Houthis, taking over Aden is a continuation of the progress they have been making. They want to show that they are strong on the ground," said Raoof Ahmed Abdullah, a Yemeni political analyst.

Aden has become a test for both sides.

Residents said hundreds of rebels have taken key sites in the advance on Aden, and appeared to be strengthening their ranks with reinforcements. The captured sites included the presidential palace, where Hadi made a final stand before fleeing, witnesses said Thursday.

Various news reports described foreign soldiers arriving in Aden's port amid fighting. Asseri denied that the coalition's forces came ashore. "We didn't have any operations in the port. This was not us," he told reporters in Riyadh.

If the reports are accurate, it could indicate foreign soldiers are arriving to evacuate more citizens from the city.

Security officials, meanwhile, told the Associated Press that al-Qaeda militants stormed a prison in Mukalla, 300 miles east of Aden, freeing about 300 inmates, including scores of militants.