The Republican nominee also said he would do "whatever you have to do to get a strong agreement," even if that meant breaking off the recently-resumed diplomatic relations.
"I just want to press -- would you break off diplomatic relations, though, on day one?" CBS4's Jim Defede asked Trump.
"I would do whatever you have to do to get a strong agreement. And people want an agreement, I like the idea of an agreement, but it has to be a real agreement. So if you call that for negotiation purposes, whatever you have to do to make a great deal for the people of Cuba," Trump said.
"Look, Cuba has to treat us fairly and it has to treat the people of Cuba fairly, and the people living here that were from Cuba or their families were from Cuba," he argued, saying the deal President Barack Obama "signed is a very weak agreement. We get nothing. The people of Cuba get nothing, and I would do whatever is necessary to get a good agreement. An agreement is fine."
Trump also responded to charges leveled in a Newsweek report from earlier this year, which alleged that he violated the US-Cuban embargo in 1998 by sending associates to explore business opportunities on the island. Further reporting from Bloomberg purported to show that additional Trump associates went in 2012 and 2013 to look at potential opportunities for a golf resort.
The Republican nominee appeared to confirm parts of the reporting, saying that he would "have to find out" if they had in fact traveled to Cuba in violation of the embargo, while acknowledging that "they had some meetings."
"I don't know exactly where they were. I can tell you that Cuba wants to, you know, really negotiate with us. They've said, 'We want to negotiate.' They want to make some kind of a deal. I've said, I don't want to make any deals unless we know we have a deal with Cuba. I think it's appropriate," he said.
"But you think they did, in fact, go to Cuba?" Defede asked.
"Well, know that Cuba wants us to go there. I'm not interested in going," Trump replied.
Defede countered, "No, I meant as emissaries -- did those individuals travel there to have those discussions?"
"I would have to find out," Trump said. "I know they had some meetings, but I would have to find out."
Under the five-decades-old US-Cuban trade embargo -- which can only be lifted by Congress -- US citizens are banned from spending any funds on the island. But while the US and Cuba restored relations in July of last year, and Obama has eased some sanctions to allow more US travel and commerce with Cuba, the embargo remains in place.
At a rally in Miami earlier in September, Trump had also blasted the Cuba policy changes, an apparent shift from past statements in which he supported the reopening of diplomatic relations after more than 50 years.