Republican presidential candidate Marco Rubio speaks during a rally on Jan. 6, 2016, in Marshalltown, Iowa. (Scott Olson/Getty Images)

Sen. Marco Rubio (R-Fla.) said he stands by a 2004 bill he co-sponsored in the Florida legislature to provide in-state tuition to undocumented immigrants, saying it was "narrowly" drafted and set specific eligibility criteria.

Rubio said Sunday on ABC's "This Week" that he "absolutely" stands by the proposal. It required undocumented immigrants to have a certain GPA, to be a graduate of a Florida high school and to have been living in the United States for a certain period to qualify for in-state tuition, he said.

"It was very narrowly tailored to high-performing students who found themselves in a situation where they were brought here by their parents when they were 5, didn't even speak another language except English and, therefore, couldn't attend college because they were being charged like they were from out of state," Rubio said. "They still had to pay for college, but they paid for what people paid when they lived in Florida."

"We didn't legalize anybody. That's the issue here," he added.

In 2014, well after Rubio left the state legislature, Florida Gov. Rick Scott (R) signed into law an initiative to provide in-state tuition for undocumented students who attended a Florida high school for at least three years.

Rubio said recent claims against the legislation are exaggerated, adding that he believes there have to be "real consequences for violating our laws."

"I continue to support and have supported and sponsored the largest border surge in American history, 20,000 new border agents, 700 miles of fencing and walls, a mandatory e-verify system, entry-exit tracking system to prevent visa overstays," Rubio said.