The White House confirmed U.S. military attacks against Al Qaeda leaders in Somalia on Tuesday as lawmakers around Washington, D.C., expressed support for the effort as a necessary action in the War on Terror.

"We can confirm that there was a military operation overnight on Sunday in Somalia," said White House spokesman Tony Snow, referring other questions on the situation to the Defense Department.

"We've made it clear that this is a global War on Terror. And this is a reiteration of the fact that people who think that they're going to try to establish a safe haven for Al Qaeda any place need to realize that we're going to fight them," Snow said.

Over at the Pentagon, spokesman Bryan Whitman confirmed that a U.S. AC-130 gunship carried out at least one air strike overnight on Sunday and said the attacks show the nation's commitment to track down terrorists.

"We're going to remain committed to reducing terrorist capabilities when and where we find them. The operation two days ago was an example of that," Whitman said, adding that the targeting "was based on credible intelligence that led us to believe that we had principal Al Qaeda leadership in an area where we could identify them and take action against them."

The air strike Monday evening was in the town of Afmadow, about 220 miles southwest of the capital of Mogadishu, Somali officials said. Five to 10 individuals were killed in the attack on in southern Somalia, a U.S. intelligence official said.

The operation marks the first U.S. mission in the East African nation since U.S. forces pulled out of Somalia in 1994. Whitman would not say whether additional air strikes have been carried out or how effective they were but did note retaliation was taken for the 1998 Al Qaeda attacks on U.S. embassies in Kenya and Tanzania.

"We are going to continue to pursue those people we believe are responsible for the embassy bombings," Whitman said.

Lawmakers defended the operation, saying it was important in the fight against terror. Sen.. Gordon Smith, R-Ore., said the effort serves as an example to go after terrorists.

"This is the way you fight the War on Terror. This is a way you hunt them out and take them out," Smith said.

"My view is we should go after terrorists wherever they are," added Sen.. Mark Pryor, D-Ark.

Pryor said it's good news to hear about attacks on some Al Qaeda leaders, but its effect won't be seen until it is known how important those leaders were in the network.

"It depends on who that is and leader of what. They may just be a little small cell leader or they could have quite a bit of influence on the African continent or even beyond that," Pryor said.

A U.S. official told FOX News that strikes may have hit Abu Talha al-Sudani, the Al Qaeda leader in East Africa. Other possible Al Qaeda operatives in Somalia include Fazul Abdullah Mohammed and Saleh ali Saleh Nabhan, also among the most wanted Al Qaeda leaders on that continent.

Rep. Adam Smith, D-Wash., said the military operation shows that the War on Terror poses challenges beyond Iraq or Afghanistan.

"The threat we face is in many, many countries and we have to be vigilant in many, many places," Smith said.

Rep. Rick Renzi, R-Ariz., who was recently in Somalia, said special operations forces are doing well in targeting training camps and some high-value targets.

An aircraft carrier and three other warships remain off the Somali coast, remaining in the region to prevent militants from escaping the area by sea, said a U.S. military official who described the actions as a sustained military operation that will continue as long as there are credible Al Qaeda targets to go after in the area.

FOX News' Mike Emanuel, Catherine Herridge and Nick Simeone and The Associated Press contributed to this report.