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A man is silhouetted near logos of the U.S. National Security Agency (NSA) and Wikipedia in this photo illustration taken in Sarajevo, Bosnia and Herzegovina, March 11, 2015. Reuters/Dado Ruvic

U.S. Sen. Rand Paul says President Barack Obama has been “disingenuous” regarding the National Security Agency's bulk data collection program. The Kentucky senator -- who announced in April that he is seeking the Republican Party's 2016 presidential nomination -- said that Obama has the authority to end the program at any time.

Paul was among other Republicans who blocked a final vote on extending government programs for collecting mobile data. He said a federal appellate court had ruled that, under the Patriot Act, the NSA program was illegal.

Paul told "CBS This Morning" that he had asked the president repeatedly to stop the program, and has wondered why Obama has not done so. Paul insisted that the request was not unreasonable on his part. He said that he was asking for two amendments and a simple majority vote on the bulk data program.

“I think sometimes my party gets all caught up in the Second Amendment [guaranteeing the right to bear arms], which is fine, but we don’t protect the Fourth Amendment enough,” Politico quoted Paul as saying. "But actually I think neither party ends up protecting the Fourth Amendment enough, which is the right to privacy,” he said.

While Paul stands against Senate Majority Leader Mitch McConnell on the issue, he said that they shared a “very personable relationship.” He admitted that both Kentucky Republicans were on opposite sides regarding the surveillance program.

Paul said that, despite differences, both senators had kept their relationship civil. They have not used harsh words against each other, he said.

The Washington Post reported that Obama had welcomed changes regarding the NSA surveillance program. The White House has been critical of Capitol Hill lawmakers for not backing the USA Freedom Act.

Paul talked about the development of Islamic State group forces as well. He said that civilized Muslims should step up against ISIS militants. When civilized Islam goes against the Islamic State group “aberration,” it is going to be the “ultimate victory,” he said.

The Obama administration has earlier warned that ending the bulk data collection program may increase the risk of terrorist attacks on the United States. Bloomberg reported that it was necessary to end the program, even temporarily, as the Senate had failed to reach agreement on the extension of key Patriot Act provisions.