Republican presidential candidate Rand Paul kicked off two weeks of fighting against surveillance with an event in Philadelphia. (Alejandro A. Alvarez/Philadelphia Inquirer via AP)

Sen. Rand Paul (R-Ky.) vowed that he would force the Patriot Act to expire Sunday when the Senate reconvenes after not taking action last week to extend or replace a controversial surveillance program.

"Tomorrow, I will force the expiration of the NSA illegal spy program," the Republican presidential candidate said in a statement, which was first reported by Politico.

The Senate will convene a rare Sunday session after it rejected a compromise bill on bulk surveillance by the National Security Agency last week. The bill would prohibit the government from engaging in the mass collection of phone records, but would leave those records in the hands of private telephone companies, which would keep them for 18 months. The Sunday session will take place hours before the Patriot Act expires.

Paul said Saturday that he would disrupt efforts to extend the Patriot Act or green light the compromise bill, known as the USA Freedom Act.

"I am ready and willing to start the debate on how we fight terrorism without giving up our liberty," Paul said in the statement. "Sometimes when the problem is big enough, you just have to start over."

Paul plans to prevent Senate Majority Leader Mitch McConnell (R-Ky.) from expediting debate on the USA Freedom Act. Even if a vast majority of senators agree to extend some version of the Patriot Act, Senate rules would allow Paul to force about five days of debate over the issue, which would lead to a temporary halt to some techniques used by the nation's spy agencies.

President Obama has called for passage of the USA Freedom Act, warning Friday in the Oval Office that gridlock in the Senate could lead to a terrorist attack.

"Heaven forbid we’ve got a problem where we could have prevented a terrorist attack or apprehended someone who was engaged in dangerous activity, but we didn’t do so simply because of inaction in the Senate," Obama said.

In his weekly address Saturday, Obama said that the USA Freedom Act has bipartisan support.

"So, what’s the problem? A small group of senators is standing in the way. And, unfortunately, some folks are trying to use this debate to score political points. But this shouldn’t and can't be about politics," Obama said.

Paul has painted his fight as a showdown against Obama and other members of the Senate, including presidential rival Ted Cruz (R-Tex.) and likely 2016 contender Lindsey O. Graham (R-S.C.), with whom Paul has repeatedly sparred over foreign policy. Paul blasted the collection of data during campaign stops in Graham's home state Friday. The Kentucky Republican's super PAC released an ad likening Sunday's vote to a pro-wrestling showdown.

"Get ready, America, for the biggest brawl for liberty of the century!" the ad said.

[Read: Rand’s ready to rumble … in a WWE-style ad slamming his GOP rivals] 

Paul's fight over surveillance is a potential inflection point for his nascent presidential campaign, which had been beset by some early stumbles. He has been conducting dozens of television interviews over the issue. His campaign has sent out flurries of Tweets and fundraising e-mails over the past week painting Paul as a politician who will stand up for Fourth Amendment rights and keep the government out of people's lives.

"My NSA spying showdown with President Obama is 24 hours away," Paul's campaign wrote Saturday in a fundraising e-mail asking for a "Money Bomb." "It may be the biggest blow ever taken against America's growing surveillance state."

[Read: Senate NSA vote underscores rift in 2016 field]

Paul and his allies spoke against NSA surveillance for nearly 11 hours on the Senate floor last week. Paul and his allies dramatically rejected a number of short-term extensions of the Patriot Act in the early morning hours of May 23, bucking McConnell. The maneuvers injected drama into the once-close relationship between Kentucky's two senators; Paul has said the two men are still friendly but disagree over this issue. McConnell has called for the Patriot Act to be renewed.

[Read: Kentucky conflict? Paul, McConnell start to clash]

In his statement Saturday, Paul said his goal is not to stymie the Senate.

"I do not do this to obstruct. I do it to build something better, more effective, more lasting, and more cognizant of who we are as Americans," he wrote.

Paul Kane contributed to this report.