Ireland’s relationship with the UK under Andy Burnham’s premiership has got off to a “very good start”, Taoiseach (Irish prime minister) Micheál Martin has said.

But he refused to be drawn on how much the issue of Irish unity had featured during their first official meeting at Number 10 North on Friday.

The visit came days after US President Donald Trump made comments about supporting a “unified Ireland”.

Martin said the men had a “broad discussion” about upholding the Good Friday Agreement and that they did not get into specifics.

“It was the first meeting, it went well… I think we have the capacity to make a lot of progress on a lot of issues in the time ahead,” he said.

Martin was the first international leader to visit the government’s new headquarters in Manchester, and also visited the Brian Boru Irish Club in Burnham’s constituency in Ashton-in-Makerfield.

On his visit to Northern Ireland last month, Burnham said a border poll was “off the table“, but later said he stood by the Good Friday Agreement.

Martin said he had “confidence” in his own approach to Northern Ireland and did not believe in promoting “rhetoric” around Irish unity.

“I understand people want to appeal to their electoral bases in Northern Ireland sometimes, but that cuts nothing in my view,” he said.

The taoiseach said he and the prime minister had discussed the UK’s Troubles legacy legislation in depth, and that he had “stressed the importance” of passing the bill through Parliament.

The government is expected to publish details of changes in the middle of next month, with Martin saying both London and Dublin had been working closely on it.

He also said both he and the prime minister wanted to see the power-sharing institutions at Stormont working more effectively, and that the Irish government believes there needs to be reform.

He said Burnham understood the issue and was currently focused on trying to resolve negotiations with the Stormont executive to agree a budget for this year.

Burnham said the relationship between the UK and Ireland matters “on every single level” as he greeted the taoiseach on Friday.

The prime minister said they were “working together” to uphold the principles of the peace deal for Northern Ireland.

Burnham added that as “co-custodians of the Good Friday Agreement, we are working together to uphold its principles as we approach the 30th anniversary”.

The Good Friday Agreement, also known as the Belfast Agreement, was a political deal designed to bring an end to 30 years of violent conflict in Northern Ireland, known as the Troubles.

The taoiseach expressed his sympathies with Burnham following the recent death of his father.

Martin said he appreciated the meeting going ahead, telling the prime minister: “I think your sense of duty shines through.”

The taoiseach said “in a global world marked by uncertainty” it was “important that two close neighbours continue the very strong engagement”.

He added: “We are co-guarantors of the Good Friday Agreement. We have very significant obligations to mind it and to progress it.”

Martin said he was also looking forward to discussing “even stronger and closer relationships between the European Union and the United Kingdom, which will be of benefit to the European Union and to Ireland”.