Gen. Dan Caine, chairman of the Joint Chiefs of Staff, said the operation in Venezuela was known as Operation Absolute Resolve and involved more than 150 aircraft across the Western Hemisphere.

Caine said it was the "culmination of months of planning and rehearsal" adding that the operation could only have been conducted by the U.S. military.

"Maduro and his wife, both indicted, gave up and were taken into custody by the Department of Justice, assisted by our incredible U.S. military with professionalism and precision, with no loss of U.S. life," Caine said.

Trump was asked by a reporter who was running Venezuela now.

"Well, we're going to be running it with a group, and we're going to make sure it's run properly," he responded.

When asked about troops on the ground, the president said, "We're not afraid of boots on the ground."

Trump said he was going to designate some people as part of the plan but did not give any specifics.

"We're going to run the country right," Trump added.

Rubio spoke about the years of prosecution and international action against the Maduro government.

"I want to be clear about one thing, Nicolas Maduro had multiple opportunities to avoid this," he said. "He was provided multiple very, very, very generous offers, and chose instead to act like a wild man."

Secretary of Defense Pete Hegseth praised the U.S. operation in Venezuela that led to the capture of President Nicolas Maduro and his wife.

He also praised Trump's leadership and praised the actions as "America first."

"As the President said, our adversaries remain on notice. America can project our will anywhere, anytime," Hegseth said.

"President Trump is deadly serious about stopping the flow of gangs and violence to our country, deadly serious about stopping the flow of drugs and poison to our people, deadly serious about getting back the oil that was stolen from us and deadly serious about reestablishing American deterrence and dominance in the Western Hemisphere," he added.

The U.S. Ambassador to the United Nations Mike Waltz, speaking to the United Nations Security Council on Monday regarding the U.S. strikes on Venezuela and capture of its president, said the U.S. is "not occupying a country."

"This was a law enforcement operation in furtherance of lawful indictments that have existed for decades," Waltz said. "The United States arrested a narco-trafficker who is now going to stand trial in the United States in accordance with the rule of law for the crimes he's committed against our people for 15 years."

Waltz also said the U.S. would not "allow the western hemisphere to be used as a base of operation for our nation's adversaries and competitors and rivals of the United States.”

The U.S. ambassador to the UN also said that President Donald Trump offered Nicolas Maduro "multiple off-ramps" and "gave diplomacy a chance."

"He tried to deescalate. Maduro refused to take them," he said. "President Trump made it clear that the narco-terrorism must stop, and yet it continued. The United States will not waver in our actions to protect Americans from the scourge of narco-terrorism and seeks peace, liberty and justice for the great people of Venezuela."

The UN Security Council meeting is ongoing.

-ABC News' Mike Pappano and Brianna Sanchez