SANAA, Yemen - Shiite rebels in control of Yemen's capital now hold the country's president "captive" at his home, his aides said Wednesday, putting in question who actually rules the Arab world's most-impoverished nation.

Embattled Abed Rabbo Mansour Hadi - a top U.S. ally in the war against al Qaeda in Yemen - appears to have run out of options to continue governing the country, months after the Houthis began a blitz in September, seizing the capital and state institutions.

The increasingly weakened leadership and power vacuum are setting stage for al Qaeda in Yemen, also known as al Qaeda in the Arabian Peninsula (AQAP), which claimed the recent attack on the French satirical newspaper Charlie Hebdo and failed assaults on the U.S. homeland, to grow more powerful in the chaos.

Hadi "cannot leave his house" after Houthi rebels removed his guards and deployed their own fighters there Wednesday, one aide said.

Another described the country being at the "point of no return." Hadi can't resign as president as the Houthis have threatened to prosecute him, that aide said.

The two aides spoke on condition of anonymity as they weren't authorized to speak to journalists.

The advisers said Wednesday that Houthis issued a list of demands to Hadi, asking for the post of vice president and several key government offices, during a meeting Tuesday with Hadi's advisers.

The Houthis say they only want an equal share of power, while critics say that they prefer presence of Hadi as a symbolic leader while they keep a grip on power.

The Houthi rebel leader, Abdel-Malek al-Houthi, warned Hadi on Tuesday that if he stalls in implementing a key U.N.-brokered deal - which effectively grants them bigger representation- "all options are open."

Al-Houthi demanded shakeup of a commission tasked with writing a draft constitution to ensure bigger representation for his group. The draft has proposed a federation of six regions, something the Houthis reject.

The collapse of Hadi's powers is rooted in Yemen's fractured armed forces, torn between Hadi and his predecessor, deposed president Ali Abdullah Saleh.

Saleh - removed from power after a 2011 uprising - is accused by many as orchestrating Houthis' seizure of Sanaa and speeding Hadi's failure. Critics also say the Houthis have the backing of regional Shiite power Iran, a charge they deny.

Capitalizing on the chaos, Saleh made a rare public statement Wednesday, urging Hadi to call for early presidential and parliamentary elections. Saleh also called for the cancellation of United Nations Security Council sanctions imposed on him and two Houthi leaders last year for "spoiling" the transition.

Saleh was granted immunity from prosecution in 2012 in return for relinquishing power in a deal brokered by Arab Gulf countries and backed by the West.

Arab countries in the Gulf Cooperation Council met Wednesday and condemned the Houthi takeover, calling it a "terrorist act" and a "coup against legitimacy." The council demanded the rebels withdraw from presidential palace.

The chaos in Sanaa prompted the U.N. Security Council to hold an emergency meeting Tuesday to condemn the violence and call for a lasting cease-fire. In a statement approved by all 15 members, the Council asserted that Hadi "is the legitimate authority" in Yemen.

The Houthis are a political and religious movement who are followers of the Shiite sect of Zaydism, who make up a third of Yemen's population of 25 million people and live mainly in the north. Sunnis live mostly in the country's south and make up two thirds of the population.

While all Houthis are Zaydis, not all Zaydis are Houthis and many are opponents to the group and its expansionist aspirations.

Saleh is a Zaydi, while Hadi is a Sunni from southern Yemen.

Some fear the Houthi offensive could fracture Yemen, only united in 1990. Political analyst Mansour Hayel said that the Houthis' power grab in the capital could prompt the "fragmentation of all of Yemen," which could become "worse than Somalia."

The violence has taken on a sectarian tone, much to the benefit of the Sunni AQAP. Over the past months, al Qaeda has launched deadly suicide bombings targeting Houthi gatherings, marking a shift in their previous tactics of targeting only security forces.

The Houthis have vowed to eradicate AQAP, and have battled the group, but they are also hostile to the U.S. Their official slogan is "Death to Israel. Death to America."

CBS News senior security contributor Mike Morrell, a former deputy director at the CIA, said on "CBS This Morning" that the risks with the Houthi rebels' advance is two-fold; it could give Iran greater influence in the already fraught Middle East, and the fighting is distracting Yemen's government from the fight against AQAP.

"What's really dangerous," said Morrell, "is that al Qaeda is now going to have space, because nobody is going to be focusing on it as these two groups fight, al Qaeda is going to have the space to grow and pose threats."

While the Houthis have been in Sanaa for months, violence escalated in recent days with the Shiite rebels kidnapping a top Hadi aide. Gun battles and mortar shelling struck Monday near the presidential palace and swept through Sanaa.

Prime Minister Khaled Bahah left his house Wednesday for another "safe place," government spokesman Rageh Badi said. His house - inside the Republican Palace - had been besieged by Houthis since Tuesday.

Meanwhile Wednesday, Houthi rebels captured a military base that houses ballistic missiles near Sanaa. Military officials, speaking on condition of anonymity as they weren't authorized to talk to journalists, said soldiers offered no resistance.

Elsewhere, authorities in Aden, the regional capital of southern Yemen, closed the airport there to protest to what local authorities described as Houthi "coup" against "national sovereignty." Local authorities also closed the port, a major hub in the Gulf of Aden.

CBS