Yemen's President Abdrabbuh Mansour Hadi has fled his palace in Aden as Houthi rebels advance towards the city.
Gunfire could be heard around the city centre, and security forces allied to the Houthis have taken over the international airport.
The rebels have made rapid gains since seizing a key airbase only 60km (37 miles) from Aden on Wednesday morning.
Government officials deny reports that the president has fled the country, and say he remains in Aden.
The US State Department says it was in touch with President Hadi earlier in the day. It said he is no longer at the compound but could not confirm any "additional details" about his location.
State television, which is controlled by the rebels, announced a reward of 20m Yemeni riyals ($93,000; £62,500) for anyone who captures the "fugitive" president.
The Reuters news agency reports that Aden residents attempted to storm an army barracks to obtain weapons before being repulsed by troops.
Yemeni Foreign Minister Riad Yassin has called on Arab nations to stage an urgent military intervention.
Analysis: Frank Gardner, BBC Security correspondent
Aden is all but surrounded. This once thriving port city that guards the southern entrance to the Red Sea is now on the verge of being overrun by Shia rebel fighters, backed by Iran and allied to soldiers loyal to Yemen's previous president Saleh.
The Shia rebels, known as 'Houthis' have swept through Yemen with extraordinary speed, alarming Saudi Arabia which fears it is being encircled by forces linked to its rival, Iran.
Today the rebels took Aden airport and a vital nearby airbase where only last week 125 US commandos were training Yemenis to fight Al-Qaida. That mission has now ended abruptly.
As Yemen descends further into chaos there are fears it could soon join Syria and Libya as another intractable war zone, attracting jihadists from many countries.
Mr Hadi took refuge in Aden last month after fleeing Sanaa, where he had been under house arrest since the rebels captured the capital.
On Wednesday morning, rebel fighters secured al-Anad air base, with the support of forces loyal to ousted former President Ali Abdullah Saleh.
US and European military advisers had been evacuated from the base last week after militants from al-Qaeda in the Arabian Peninsula (AQAP) overran a nearby town.
Hours after the rebels captured the base, unidentified warplanes targeted the palace compound in Aden, officials and witnesses said, in the third such attack in a week.
Soon afterwards, a source in the presidential guard told the AFP news agency that Mr Hadi had boarded a helicopter for "an unknown destination abroad".
But senior aides to Mr Hadi insisted he had merely been transferred to a "secure location within Aden" and had no plans to leave.
Meanwhile, Houthi officials said its fighters had arrested the country's Defence Minister, Mahmoud al-Subaihi, and a senior aide in the southern city of Lahj.
The Zaidi Shia-led rebels have said their aim is to replace Mr Hadi's government, which they accuse of being corrupt, and to implement the outcomes of the National Dialogue that was convened when Mr Saleh was forced to hand over power in 2011 following mass protests.
The Houthis swept southwards from their northern heartland of Saada province last summer, entering the capital in September.
They have since pushed into central, western and southern provinces with the support of Mr Saleh's allies, sparking clashes with Sunni tribesmen, AQAP militants and southern separatists.
The Houthis: Zaidi Shia-led rebels from the north, who seized control of Sanaa last year and have since been expanding their control
President Hadi: Backed by military and police loyalists, and by militia known as Popular Resistance Committees, he is trying to fight back against the rebels from his stronghold in the south
Al-Qaeda in the Arabian Peninsula: Seen by the US as the most dangerous offshoot of al-Qaeda, AQAP opposes both the Houthis and President Hadi.
Islamic State: A Yemeni affiliate of IS has recently emerged, seeking to eclipse AQAP.