Northern Ireland First Minister Arlene Foster has said she is pleased that the Brexit vote has been respected, but can understand that many people will not be celebrating.

Speaking on RTÉ's Late Late Show, Mrs Foster said "a lot of people will be sad" that Britain is formally leaving the European Union.

The DUP leader said she wants to send out a message that the Republic of Ireland and the United Kingdom will continue to be neighbours despite Brexit.

Mrs Foster said "whilst we're leaving the institutions of the European Union, we're not leaving Europe and we're certainly not leaving the island of Ireland.

"We will continue to have those neighbourly relationships."

Mrs Foster said that while she is pleased that Northern Ireland was leaving the EU, she said she is "concerned also about the fact that obviously we're not leaving on the same terms as the rest of the United Kingdom, there are still issues to be dealt with."

However she said she "understands very much the anxiety of people who wish to remain in the European Union institutions".

Mrs Foster said: "The Brexit debate has been very polarising" not just in Northern Ireland, but right across the United Kingdom.

"So the first thing to do is not to be triumphalist and actually to acknowledge that people don't want this to happen and I do acknowledge that."

But, she said, "the communities that live along the border, will still be the communities that live along the border" despite the UK's departure from the EU.

Mrs Foster said she now wants to work with colleagues and the newly formed Northern Ireland Executive "to find the common ground between us all".

She said she believed people voted to leave the European Union "because they felt disconnected from the institutions."

She also said the idea of a border down the Irish Sea "rankles" with her and there is a lot of work still to do on the issue.

"Boris Johnson, the Prime Minister, says that emphatically there won't be any checks, and then I listen to Michel Barnier, he says something very, very different. So there's a lot of work to do on all of that." 

Mrs Foster was also asked about her attendance at the funeral of former Northern Ireland Deputy First Minister Martin McGuinness in 2017.

She said "it was absolutely the right thing to do".

However, she admitted that she lost friends over her decision to attend the funeral.

She said she was "obviously apprehensive" about going because she wasn't sure what reception she would receive.

"But I have to say I was welcomed very warmly," she added.

On the issue of same-sex marriage, she it is wrong that it was "imposed" on Northern Ireland by Westminster and the matter should have been left to the NI Assembly to decide.

"I think there was a majority in the Assembly for same sex-marriage and I think it would have come into being."

Asked about her opposition to same-sex marriage, Mrs Foster said: "I think marriage is between a man and a woman", adding, "there are other partnerships."

Asked about the so-called "cash for ash" inquiry in Northern Ireland, Mrs Foster said she believes she will still be First Minister after the report is published.

She said she welcomes the inquiry and the report.

She rejected that there was any corruption, incompetence or cover up involved in the Renewable Heat Incentive Scheme.

Mrs Foster also said she does not think a United Ireland will be a reality.

She said: "I don't think that it is going to happen".

"There are many reasons why we will stay in the United Kingdom - economic, social, political and cultural".

And she said she would be "absolutely devastated" about leaving the United Kingdom because "I'm a unionist".

She said she wants Northern Ireland to be a better place for everyone regardless of their sexuality or religion.

"Just because we have different views on different things, doesn't mean that we can't find common ground, to work, to move forward and to make Northern Ireland work," she added.