After their disagreement over immigration, presidential hopefuls Florida Sen. Marco Rubio and Texas Sen. Ted Cruz this week turned to matters of national security, but continued their headline-grabbing infighting.

Rubio, who sits on the Senate's Foreign Relations and Intelligence committees, accused Cruz of trying to cut the military budget and gut the nation's intelligence programs, The New York Times reported.

"On some of the defense issues, we've parted ways," the Floridian noted. "For the first few years in the Senate that he's been there, he's voted for budgets that have hurt the military. He voted for a budget that basically gutted our foreign aid program, particularly our defense of the Israelis and of aid that we provided them."

The Texas senator, for his part, minced no words when he countered Rubio's latest attack, dubbing it "a lot of silliness," The Hill noted.

"In many ways, it's a backhanded compliment," Cruz said, claiming that such criticism suggests Rubio sees him as a formidable challenger in the race for the GOP nomination. "If they're not shooting at you, you're not doing much of anything." 

Nevertheless, Cruz tried to bring the focus back to the controversial immigration issue, Politico pointed out. He has hammered Rubio over his support for a 2013 comprehensive bill that would have given undocumented migrants in the United States a pathway to citizenship.

"It is not surprising that [Rubio's] campaign wants to change the topic from [Rubio's] partnership with President Obama to push a massive amnesty program," he said. "I understand politically why they want to change the topic from that, but I don't think they're going to be successful."

Despite the back-and-forth, Rubio insisted in a Wednesday interview with radio host Hugh Hewitt that his disagreements with Cruz were based on the issues and that his Senate colleague was "someone I like personally"

"We get along," Rubio said about their relationship. "We share a lot of views."