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 neighboring Saudi Arabia.

But the rebel forces, which already control the capital, ­Sanaa, 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 what have been 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 that pro-Hadi groups in the city, called Popular Committees, appeared to have largely disbanded or fallen back during the fighting. The Shiite rebels, known as Houthis, and their allied fighters reached as far as the central district of Crater — 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 ragtag militias, offering a guerrilla-style defense of the last major foothold of Hadi’s government.

Control of Aden would earn the rebels another gain: a staging ground to try to take 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.

Shiite rebels known as Houthis hold up their weapons to protest against Saudi-led airstrikes, during a rally in Sanaa, Yemen, Wednesday, April 1, 2015. (AP Photo/Hani Mohammed) (Hani Mohammed/AP)

“The Houthis have surrounded the palace. It’s theirs,” said Ali al-Maamari, 31, an information-technology employee in Aden who lives near the palace.

Warplanes from the Saudi-led coalition, meanwhile, seek to target supply lines and rebel camps around Aden, said a spokesman, Brig. Gen. Ahmed Asseri in Riyadh, Saudi Arabia. But the alliance is wary about shifting airstrikes into populated areas, fearing rising civilian casualties.

Yemen’s deepening conflict is essentially a struggle between groups favored by Saudi Arabia, the traditional power broker in Yemen, and factions that resist the kingdom’s influence. At the same time, the violence has effectively wiped away central power in a country splintered among other militant groups, such as al-Qaeda and those claiming loyalty to the Islamic State.

But the battles have also taken on the contours of a regional showdown pitting Saudi Arabia and its Sunni Arab allies against Shiite power Iran. Tehran is believed to back the Houthis and has strongly condemned the ­Saudi-led air campaign, which has been blamed for growing civilian casualties.

Various news reports described foreign soldiers arriving in Aden’s port amid the fighting. But 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 arriving to evacuate more citizens from the city.

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

The officials said the al-Qaeda militants were deployed Thursday across major roads leading into Mukalla in an apparent bid to thwart any attempt to retake the city, the AP reported.

Saudi Arabia has massed ground troops along its southern border with Yemen, but Asseri said there were no imminent plans to move into Yemen.

In Washington, a senior U.S. military official speaking with reporters Thursday also played down the possibility of a Saudi ground invasion.

“I don’t think they’re going to do that. I think they’re arraying their forces along the border to prevent a Houthi incursion,” the official said, speaking on the condition of anonymity. “They’re postured defensively.”

Asseri said one Saudi border soldier had been killed and five were wounded in cross-border gunfire Thursday. The official Saudi Press Agency said that Saudi forces had fired back into Yemen.

The Houthi forces appear to have gained allies among soldiers loyal to Yemen’s former president Ali Abdullah Saleh. Saleh, who was forced from power by protests in 2011, took refuge in Saudi Arabia after being burned in a bombing of his compound in Sanaa.

Saleh denies accusations that he has aided the Houthis. He has blamed Yemen’s instability on Hadi, who developed ties with the United States to assist with drone strikes and other measures against the powerful al-Qaeda branch in Yemen.

Houthi leaders also deny any collusion with Saleh. But diplomats and analysts say that coordination between Saleh and the Houthis was crucial for the rebel takeover of much of Sanaa in September. They say Saleh called on loyal officers to stand down, allowing the Houthis to sweep into the capital.

Murphy reported from Riyadh. Hugh Naylor in Beirut and Erin Cunningham in Cairo contributed to this report.

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