The group of pirates holding Phillips in the Indian ocean since Wednesday have said that will kill the hostage and fight back if any of the vessels tracking the lifeboat, including the USS Bainbridge, were to attack.
The US Bainbridge, equipped with a surveillance plane, was preventing the pirates from moving their hostage to a larger ship.
Two US warships, including a counter-piracy task force from Bahrain, are on their way to join the Bainbridge which has been circling the lifeboat.
"The safe return of the captain is the top priority," Robert Gates, US defence secretary, said in Washington.
This incident marks the first time that Somali pirates have captured an American.
Phillips had been held since Wednesday when his ship, Maersk Alabama, which was carrying food aid for Uganda and Somalia, was hijacked while on a humanitarian mission.
Hundreds of hostages
Phillips is one of about 270 hostages currently held by Somali pirates preying on the busy waters of the Gulf of Aden and Indian Ocean for years.
Last year 42 ships were hijacked, disrupting food aid to Africa and increasing insurance costs.
In the past week, Somali pirates have hijacked a US container ship, a British-owned Italian-operated, a small French sailing yacht, cargo, a German container carrier, a Taiwanese fishing vessel and a Yemeni tugboat.
Late last year, a Ukrainian cargo loaded with tanks and other weapons and a Saudi super-tanker carrying $100 million of crude oil were captured by the pirates, who were reportedly paid about $8 million in ransom.