Taoiseach (Irish prime minister) Micheál Martin has told Prime Minister Andy Burnham their governments have a duty to “mind and progress” the 1998 Good Friday Agreement.

Burnham said the relationship between the UK and Ireland matters “on every single level” as they met at Number 10 North for talks on Friday.

The pair were expected to discuss a further strengthening of ties including boosting trade, security and working with the European Union.

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

Speaking ahead of their talks, Burnham said it “feels very fitting” to welcome Martin as the first international visitor to Number 10 North in Manchester.

“The relationship between the UK and Ireland matters so much on every single level,” he said.

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 and so forth.”

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”.

A Downing Street spokesperson said the two leaders began by “reaffirming the close partnership between the UK and Ireland, as well as their shared commitment to upholding the Good Friday Agreement”.

They also discussed the legacy of the Troubles and “working towards lasting reconciliation in Northern Ireland”.

Other topics included the UK’s closer relationship with Europe, their joint support for Ukraine, and looked ahead the UK’s hosting of the next UK-Ireland Summit next year.