Sen. Rand Paul (R-Ky.) announced Thursday that he is taking steps toward bringing legal action against the government over its sweeping surveillance efforts.

"The president said he want a debate. It starts today," Paul said at a Capitol Hill news conference, where he was joined by a handful of lawmakers as well as representatives from the American Civil Liberties Union and the conservative group FreedomWorks, among others.

Sweeping telephone record and Internet surveillance efforts by the National Security Agency were recently revealed by The Washington Post and Britain's Guardian newspaper.

Paul announced Sunday that he planned to file a class action lawsuit and discussed his intention in a subsequent interview on Wednesday, so Thursday's announcement was not a surprise.

"Well, we are asking people who have been affected by this spying if they want to sue the government and say, you know what, this is unconstitutional," Paul told Fox News Channel on Wednesday. "And since everyone's phone records were spied upon, I would guess that that includes millions and millions of people. ... So what we're saying is, is that the government has no right through a single warrant to search everyone's records."

Paul said Thursday that more than 250,000 people have signed on to a petition indicating an intent to be part of a lawsuit.

The ACLU filed a lawsuit Tuesday that challenges the constitutionality of the surveillance effort that collects the telephone records of millions of Americans.

Paul is still exploring the specific avenues through which he can file a lawsuit. For example, Paul said he is still working to determine whether he can join other lawsuits. For now, he said, the goal is to provide Americans who share his concerns with a gathering point.

"Right now we are a portal for people to come and collect and say we are unhappy with what the government's doing with our privacy," he said.

The senator said that discourse about the government's surveillance efforts is a good thing, not a harmful development.

"What would be wrong is if someone released the computer programming code about how we are doing this -- that's a secret," he said.