The ship's owners say securing Capt Phillips' release is their priority
The hijacked US ship freed by its crew has reportedly set sail for Kenya, but its captain remains adrift in a lifeboat held by pirates.
Relatives of the US crew on board the Maersk Alabama cargo ship said it was sailing to Mombasa under armed guard.
FBI experts are helping in negotiations and a US warship remains near the scene where pirates continue to hold Capt Richard Phillips hostage.
The US crew retook the boat after a long struggle on Wednesday.
Capt Phillips' relatives say they have been told he offered himself as a hostage to save his crew.
Ship 'on the move'
The US Navy despatched the cruise-missile carrying USS Bainbridge to the scene on Wednesday along with several other vessels.
An official said the destroyer was staying where the pirates could see it.
On Thursday the US military announced it would deploy more forces to the Horn of Africa to help deal with the stand-off.
General David Petraeus said forces would arrive within 48 hours "to ensure that we have all the capability that might be needed over the course of the coming days".
Maersk spokesman Kevin Speers says Capt Richard Phillips "remains unharmed"
There are thought to be four pirates in the lifeboat with Capt Phillips, and it is not yet clear what they are demanding.
The ship's owners, a US subsidiary of the Danish logistics giant Maersk, have been holding regular briefings with the relatives of the sailors on board the vessel.
On Thursday Joseph Murphy, whose son Shane is second in command, said Maersk officials had told him the ship was now sailing for Mombasa.
A sailor on the Maersk Alabama confirmed to the Associated Press news agency that the ship was on the move.
'Playing with fire'
Analysts have said negotiations could be lengthy, with the pirates likely to want a hefty ransom for the captain as well as compensation for a boat that was wrecked in the attack.
And the lifeboat is thought to be equipped for a week at sea, although officials said it had now run out of petrol.
The cargo ship, carrying food aid destined for Somalia and Uganda, was taken about 500km (311 miles) off Somalia's coast in the early hours of Wednesday.
Mohamed Omaar, the foreign minister in Somalia's fragile transitional government, told AP that the pirates were "playing with fire".
He said they had "got themselves into a situation where they have to extricate themselves because there is no way they can win".
Somalia has been without an effective government since 1991, fuelling the lawlessness which has allowed the pirates to thrive.
On Wednesday, sailors on the Maersk Alabama managed to give US media dramatic accounts of their day-long battle with the pirates.
According to second mate Ken Quinn, the crew managed to capture one of the pirates and keep him tied up for 12 hours while they attempted to negotiate the release of their captain.
Pirates typically hold the ships and crews until large ransoms are paid by the shipping companies - last year the firms handed over about $80m (£54m).
After a lull earlier this year, this was the sixth ship seized off Somalia in the past week.
The attacks are threatening to destabilise one of the world's busiest shipping lanes.