"I think we've got to be prepared to take aggressive military action against the Iranians to stop them from killing Americans in Iraq," Lieberman said. "And to me, that would include a strike over the border into Iran, where we have good evidence that they have a base at which they are training these people coming back into Iraq to kill our soldiers."

The U.S. accuses Iran of fostering terrorism and Tehran's nuclear ambitions have brought about international reproach.

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Lieberman, the Democratic nominee for vice president in 2000 who now represents Connecticut as an independent, spoke of Iranians' role in the continued violence in Iraq.

"We've said so publicly that the Iranians have a base in Iran at which they are training Iraqis who are coming in and killing Americans. By some estimates, they have killed as many as 200 American soldiers," Lieberman said. "Well, we can tell them we want them to stop that. But if there's any hope of the Iranians living according to the international rule of law and stopping, for instance, their nuclear weapons development, we can't just talk to them."

He added, "If they don't play by the rules, we've got to use our force, and to me, that would include taking military action to stop them from doing what they're doing."

Lieberman said much of the action could probably be done by air, although he would leave the strategy to the generals in charge. "I want to make clear I'm not talking about a massive ground invasion of Iran," Lieberman said.

"They can't believe that they have immunity for training and equipping people to come in and kill Americans," he said. "We cannot let them get away with it. If we do, they'll take that as a sign of weakness on our part and we will pay for it in Iraq and throughout the region and ultimately right here at home."

To deal with Iran's nuclear ambitions, Democratic presidential hopeful Bill Richardson said tough negotiation is called for.

"I would talk to them, but I would build an international coalition that would promote and push economic sanctions on them," Richardson said. "Sanctions would work on Iran. They are susceptible to disinvestment policy. They are susceptible to cuts, economic sanctions in commodities."

On Friday, Secretary of State Condoleezza Rice said Iran's detention of at least four Americans is unwarranted but will not stop Washington from trying to engage Iran on other matters, including its disputed nuclear program and alleged support of insurgents in Iraq.

In an Associated Press interview, Rice also appeared to cast doubt on whether the U.S. would take its tentative diplomatic outreach to Iran any further for now.

The U.S. and Iranian ambassadors in Iraq met last month for the first public, substantive high-level discussions the two countries have held in nearly three decades. Although limited to the topic of violence and instability in Iraq, the talks have been seen as a possible window to better relations.

Immediately after the meeting in Baghdad, Iran announced plans for another. But U.S. Ambassador Ryan Crocker said Washington would decide only after the Iraqi government issued an invitation.

U.S. officials also said they wanted to see Iran follow up on U.S. complaints that it is equipping and helping insurgents who attack American forces.

Lieberman spoke on "Face the Nation" on CBS. Richardson was on "Late Edition" on CNN.