The health secretary, Matt Hancock, has said the UK could hold a second referendum on Brexit if MPs vote against Theresa May’s withdrawal agreement.

Speaking on ITV’s Good Morning Britain, he said he was “dead set against” the idea of another vote on the UK’s membership of the EU, but could not rule it out.

“If it doesn’t go through, whether we end up with no deal or second referendum is impossible to know. I think that everybody should vote for the deal because it is in the national interest,” Hancock said of the prime minister’s deal.

Asked to rule out the possibility of a second referendum, he said: “I’m certainly ruling out me supporting it.”

Hancock told the programme: “I think a second referendum would be terrible. It would be incredibly divisive. Think of how divisive the debate about Brexit has been over the last few years. For a second referendum, that would be even worse.

“But it wouldn’t be decisive either, because if the system had rejected the result of the first referendum, why should people accept the result of the second? I think that is a complete mistake.”

Hancock also claimed May had made “further progress” on the UK’s future partnership with the EU in negotiations in Brussels this week, ahead of a planned EU summit on Sunday.

When it was put to him that European leaders have insisted they cannot budge further on the deal, the minister said: “The progress is on the future partnership. The part that is agreed is the withdrawal agreement, which is essentially how we technically leave.”

And he claimed that what May had secured this week would help ensure more MPs back the deal in a vote in the House of Commons next month.

“The whole package includes the work that is being negotiated this week on the future relationship,” Hancock said.

“It is the future relationship element of this deal which will define our relationship with the EU for the years and the decades to come. The withdrawal agreement is about how we leave. And the whole thing will go to parliament as a package. I think it is a good deal.”