A spokesman for the ship company Maersk, Kevin Speers, told AP Radio that the destroyer USS Bainbridge was on the scene. He added that the boat with the pirates is floating near the Maersk Alabama.
Speers said Wednesday night that dawn is only a few hours away in Somalia and officials are waiting to see what happens when the sun comes up.
The Maersk Alabama is the first ship with an American crew to be taken by pirates off the Horn of Africa. Crew members were negotiating with the pirates for the return of their captain.
The Bainbridge was among several U.S. ships, including the cruiser USS Gettysburg, that had been patrolling in the region.
Speers confirmed earlier Wednesday that the crew had the Maersk Alabama and were unharmed but the captain was being held by pirates off the cargo ship.
"They're on another boat," he said. He gave no other details.
The second in command, Shane Murphy of Seekonk, Massachusetts, called his wife at 10 a.m EDT and told her that pirates had taken over the ship before dawn local time, she said.
Murphy said that pirates then had taken away the captain and he was now in charge, Serena Murphy, 31, told The Associated Press from her front doorstep.
Shane Murphy's father, Capt. Joseph Murphy, an instructor at the Massachusetts Maritime Academy, told the AP that he was called by the Department of Defense and told the crew, including his son Shane, had control of the ship back from the pirates.
CBS News national security correspondent David Martin reports that according to Murphy, it began with a sea chase.
"They outran the pirates for between three and five hours," Murphy said. "They were finally overtaken, substantial gunfire involved."
The vessel had 20 U.S. nationals onboard before the hijacking, Maersk said.
Andrea Phillips, the wife of Capt. Richard Phillips of Underhill, Vermont, said her husband had sailed in the waters off Somalia "for quite some time" and a hijacking was perhaps "inevitable."
A crewmember told CBS News that Captain Phillips gave himself up to the pirates.
A U.S. Navy surveillance plane has now spotted the lifeboat holding Phillips and the four pirates, reports Martin. A rescue mission could easily cost the captain his life, so the plan is to convince the pirates their situation is hopeless and they have no choice but to surrender.
In an exclusive call to the ship, crewmember Ken Quinn told CBS News about how the pirates tried to seize control.
"There were four Somali pirates with AK-47s," Quinn said. "We took one of them hostage in the steering gear room with us and then the other three the captain talked them into getting into a life boat. But now they got our captain (in a) lifeboat. And they got him hostage. They wanted an American captain to hold for ransom. And we're trying to run them down and get them back right now. That's the what - that's the whole story. I've gotta go. I'm piloting the ship."
Colin Wright, who identified himself as a third mate aboard the ship, told the AP by phone that, "Somalian pirates have one of our crew members in our lifeboat and we are trying to recover that crew member."
At one point, the pirates had held the boat and the entire crew of Americans. Wright said: "We're really busy right now, but you can call back in an hour or two."
President Barack Obama was following the situation closely, foreign policy adviser Denis McDonough said.
U.S. officials said an American Navy destroyer, the USS Bainbridge, was headed for the scene along with at least six other vessels. The Bainbridge was among several U.S. ships, including the cruiser USS Gettysburg, that had been patrolling in the region but were several hours away when the Maersk Alabama was seized.
The Bainbridge is a guided missile destroyer carrying Tomahawk cruise missiles, torpedoes and two MH-60 Knighthawk helicopters armed with Hellfire missiles.
It was not clear what the military crews would do when they got there. Options could include negotiation, backed by force.
The ship was carrying emergency food relief to Mombasa, Kenya, when it was hijacked, the Copenhagen-based container shipping group A.P. Moller-Maersk said.
Merchant crews aren't supposed to fight pirates, short of using high-pressure hoses to try to stop them from climbing aboard, said John F. Reinhart, president and CEO of Maersk Line Ltd.
"They (the crews) don't have any weapons, so it would be inappropriate for them to try to be heroes. We'd like them to come home safely," he told a news conference.
It was the sixth vessel seized within a week, a rise that analysts attribute to a new strategy by Somali pirates who are operating far from the warships patrolling the Gulf of Aden.
In speedboats, guided by satellite navigation devices and armed with light weapons, pirates using grappling hooks and rope ladders can board a target and take over an unarmed crew in minutes - with huge profit when they get away with it, reports CBS News correspondent Richard Roth.
Cmdr. Jane Campbell, a spokeswoman for the U.S. Navy's Bahrain-based 5th Fleet, said that it was the first pirate attack "involving U.S. nationals and a U.S.-flagged vessel in recent memory." She did not give an exact timeframe.
Joseph Murphy, a professor at the Massachusetts Maritime Academy, said his son was a 2001 graduate who recently talked to a class about the dangers of piracy.
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Somali pirates are trained fighters who frequently dress in military fatigues and use speedboats equipped with satellite phones and GPS equipment. They are typically armed with automatic weapons, anti-tank rocket launchers and various types of grenades. Far out to sea, their speedboats operate from larger mother ships.
The U.S. Navy said that the ship was hijacked early Wednesday about 280 miles (450 kilometers) southeast of Eyl, a town in the northern Puntland region of Somalia.
U.S. Navy spokesman Lt. Nathan Christensen said the closest U.S. ship at the time of the hijacking was 345 miles (555 kilometers)away.
The Combined Maritime Forces issued an advisory Wednesday highlighting several recent attacks that occurred hundreds of miles off the Somali coast and stating that merchant mariners should be increasingly vigilant when operating in those waters.
Since January, pirates have staged 66 attacks, and they are still holding 14 ships and 260 crew members as hostages, according to the International Maritime Bureau, a watchdog group based in Kuala Lumpur.
There are fewer than 200 U.S.-flagged vessels in international waters, said Larry Howard, chair of the Global Business and Transportation Department at SUNY Maritime College in New York.