Marco Rubio, the Florida senator who this week declared his candidacy for the Republican presidential nomination in 2016, on Sunday said he did not “believe same-sex marriage is a constitutional right”.

Rubio said instead that the issue should be decided at the state level, although he did concede that “sexual preference is something that people are born with”.

Same-sex marriage is now legal in 37 US states – including Florida – and the District of Columbia, a situation reached after the supreme court struck down the Defense of Marriage Act (Doma) in 2013. The issue remains contentious in many southern states, but a final supreme court decision on its constitutionality is expected this month.

“It’s not that I’m against gay marriage,” Rubio said in a CBS interview taped in New Hampshire, the early voting state to which Republican candidates flocked this weekend. “I believe the definition of the institution of marriage should be between one man and one woman.

“States have always regulated marriage. And if a state wants to have a different definition, you should petition the state legislature and have a political debate. I don’t think courts should be making that decision.”

“I don’t believe same-sex marriage is a constitutional right. I also don’t believe that your sexual preferences are a choice for the vast and enormous majority of people. In fact … I believe that sexual preference is something that people are born with.”

Before and after his declaration of his presidential candidacy, Rubio’s views on a number of nationally contested issues have come under close scrutiny. Though he acknowledges the existence of climate change – in contrast to many other prominent Republicans – he has said that he does not believe it is caused by humans.

The son of Cuban immigrants was also asked about immigration, another issue on which Republican feelings run high. In 2013 he was one of the sponsors of a comprehensive reform bill. Many critics have suggested he dropped the issue after the bill’s failure to pass through Congress.

Rubio told CBS host Bob Schieffer he no longer believed such an approach could work, and instead outlined a number of steps he said would have to be taken – on issues such as border security – before undocumented immigrants in the US could achieve citizenship.

“We understand that we have to deal with 12 million human beings that are in this country, that have been here for longer than a decade,” he said. “We know we have to deal with this. We are not prepared to deal with it until first you can prove to us this will never happen again.”

Asked about his position in a crowded Republican field – potentially featuring as many as 19 candidates for the nomination – Rubio said he was uniquely qualified having served at local, state and national levels.

Repeating familiar attack lines heard across the field in Nashua, New Hampshire, on Friday and Saturday, he also said Democratic presidential candidate Hillary Clinton would offer the country “another four years of Barack Obama”, and her record on foreign policy had been “a disaster for America”.

At his campaign launch on Tuesday, Rubio played heavily on his youth as compared with Clinton’s age, which is 67. In response to scepticism surrounding his experience, as he runs for the White House after less than one full term on Capitol Hill, the 43-year-old told CBS: “The presidency’s a big job and I’m prepared for that.”