CAIRO — Libyan rebels battled Monday to hold Tripoli as Moammar Gadhafi's son and longtime heir apparent — whom the rebels claimed to have captured — made a surprise appearance outside a hotel and dismissed claims that his father had lost control of the country.

That Seif al-Islam Gadhafi was in fact free — and not in their custody, as they'd bragged Sunday — wasn't just a tremendous embarrassment for the rebels. It also raised serious questions about the credibility of the opposition government set to take control of post-Gadhafi Libya and, more urgently, about the rebels' claims to control nearly all of the capital.

Seif al-Islam's purported arrest had signaled the imminent end of the regime, and it wasn't clear whether he was escaped from custody or was never captured at all. Rebel leaders didn't immediately explain what happened, and the White House had no immediate comment.

Just a day earlier, the International Criminal Court had said it would ask the rebels to transfer Seif al-Islam to its custody to try him for crimes against humanity. Late Monday, Arabic satellite channels showed the son swaggering out of an armored SUV outside a hotel housing foreign journalists shortly after midnight local time, wearing a scruffy beard and an army green t-shirt, shaking hands with supporters and saying, "Things are fine in Tripoli."

News services reported that Seif al-Islam then took some foreign journalists on a tour of parts of Tripoli under Gadhafi's control and suggested that government forces had allowed the rebels to enter Tripoli as a plot to entrap them.

The news cast a pall of uncertainty over a day in which rebels battled to consolidate their grip on the capital even as they clashed with pro-Gadhafi holdouts at his Bab al Azizya compound in southern Tripoli. Another Gadhafi son, Mohammed, reportedly escaped rebel custody in unclear circumstances. And residents in Zuwara, a town west of Tripoli and about 30 miles from the Tunisian border, reported heavy shelling from three nearby towns believed to be loyal to the longtime ruler.

Anees al Fonas, a member of the rebel media council from Zuwara who spoke by phone from Tunisia, said that rockets and mortars had been fired "for the last 24 hours, nonstop," from the nearby towns of Zolton, Riqdalin and Al Jamil. One civilian was killed Monday when a rocket landed on the roof of his house, and four others were injured, Fonas said.

A small group of rebels were on the outskirts of Zuwara, but reinforcements from rebel-held Sabrata, about 25 miles to the east, could not arrive because Gadhafi forces reportedly were stationed near a road connecting the two.

President Barack Obama called for a "peaceful, inclusive and just" transition but warned that the situation "is still very fluid." The six-month fight against Gadhafi, aided by a NATO-led coalition, turned in favor of the rebels only in the past two weeks, and took far longer than the Arab Spring revolutions in neighboring Egypt and Tunisia.

Still, Obama, who was vacationing in Martha's Vineyard, Mass., told rebels that "the Libya you deserve is within your reach." And residents reached by phone said that much of Tripoli appeared to be in opposition hands, with rebels and volunteers setting up checkpoints, deploying civilian patrols and securing buildings.