The Department of Justice is deciding what to do with the captive pirate -- whether to send him to Kenya for prosecution as other pirates have been, or whether to try him in the United States because he was pirating a U.S. vessel.
Though the Pentagon directed the military response to the crisis, President Obama was personally involved.
After the rescue, Obama's statement said the battle against pirates would not end.
"We remain resolved to halt the rise of piracy in this region," Obama said. "To achieve that goal, we must continue to work with our partners to prevent future attacks, be prepared to interdict acts of piracy and ensure that those who commit acts of piracy are held accountable for their crimes."
On "Fox News Sunday," before it was known Phillips was safe, Sen. Tom Coburn, R-Okla., said the United States must not back down to the pirates.
"You have to have a tough approach," he said, "which means you have to be strong. We're not going to give in to blackmail and we're not gonna allow them to continue to do what they're doing."
On the same show, Sen. Evan Bayh, D-Ind., sounded a similar note.
"Once we've resolved the situation with the captain, we don't want to imperil his life, we've got to make them pay a price for this kind of activity that is larger than the ransoms they're extracting so they'll discontinue it," he said.
But the question was how to stop future attacks.
On ABC News' "This Week," Adm. Thad Allen, the commandant of the U.S. Coast Guard, said the answer is not arming merchant ships to defend against pirates, as some have advocated.
"I think that's pretty problematic for reasons such as training, certification, how you apply standards," he said. "The discussions I've had with the private sector and the ship companies really don't favor that right now."
Kaj Larsen, a former Navy SEAL who has made documentaries on pirates in Indonesia and arms sales in Mogadishu, told ABC News the problem of piracy will not be easily solved.
"I'm very relieved that the hostage is safe," Larsen said. "That was a happy ending to what was obviously a trying ordeal for the American crew. At the same time I'm cautiously pessimistic, because I'm keenly aware that we're going to see more and more of this problem in the future.
"I don't think in this particular case unfortunately, you're going to see a deterrent effect," he said. "The sums that these pirates are making are just extraordinary. So the incentive is too great even if they lose a few of their foot soldiers in the process."
Before Phillips was rescued, his fate was far from certain. In fact, there were reports earlier in the day that negotiations for Phillips' release had broken down.
Somali elders who were negotiating for the pirates offered to forgo a ransom but insisted that the pirates not be arrested, according to people in touch with the elders. However, the U.S. negotiators would not accept those terms, the sources said.
This morning, the U.S. military said its negotiators were continuing their efforts.
Until the rescue, Phillips and his captors were in a lifeboat off the African coast after leaving the Maersk Alabama on Wednesday.
Three U.S. Navy warships were trying to prevent them from reaching the Somali coast. The USS Halyburton and USS Bainbridge were sticking with the lifeboat. A third ship, the USS Boxer, was farther away but still within helicopter range.