Hopes that Brexit talks between the EU and the UK could restart after nine months of paralysis were raised over the weekend after Northern Ireland minister Conor Burns held talks with the European Commission vice-president Maroš Šefčovič.

He spoke as the Irish prime minister, Micheál Martin, said the deepening row over the Brexit arrangements for Northern Ireland was “testing and fraying” Anglo-Irish relations, but that the arrival of a new prime minister offered a chance for a fresh approach to break the impasse.

Burns met Šefčovič over the weekend in the sidelines of the British Irish Association conference at Oxford University and will be advising the new prime minister that conditions could be right to reopen negotiations, put on hold last February.

“In light of today, I will certainly send advice to them and that advice will be that I think there could well be the appetite to have another go of this,” he said.

The protracted row over the Northern Ireland protocol has ruptured relations with the EU and has led to the near collapse of the Stormont assembly, with the Democratic Unionist party refusing to re-enter the executive government until the Brexit arrangements for the country change.

The EU is fully expecting Truss to press ahead with the Northern Ireland protocol bill. But British sources have pointed out that even if article 16 is triggered, which allows one side to in effect unilaterally suspend provisions in the Brexit deal, the legislation that will enable the government to rip up part of the protocol will not go to the House of Lords until mid-October at the earliest. This leaves a six-week window in which pre-talks could take place.

Martin told a conference in Oxford on Saturday that the next two weeks would be critical and he was hoping the new Conservative party leader, likely to be Liz Truss, would send a “serious signal” that he or she wanted to put the dispute behind them.

Forging ahead with legislation to tear up the protocol would be seen as a hostile move but it would not exclude the possibility of parallel talks, sources have said.

“Unilateralism does not work. It fosters suspicion and distrust. We believe there is an opportunity with the election of a new prime minister to create a window of opportunity for a new spirit that will allow for negotiations,” he said.

The EU and the UK government have expressed their determination to resolve the row through negotiations, but some have described their pleadings as “the dialogue of the deaf” with both sides travelling on parallel tracks.

The UK looks likely to take a firm line rather than strike a conciliatory note next week.

On Friday the Northern Ireland secretary, Shailesh Vara, indicated that there would be no pulling back and that the UK needed to have the legislation in place as an “insurance policy” and Truss is reportedly considering triggering article 16, which would signal no weakening of position to the Eurosceptic wing of the Tory party.

“Regrettably, unilateral action on the protocol and on legacy is at odds with the spirit of partnership that is needed to underpin the Good Friday agreement,” Martin told the British Irish Association conference.

“It is testing and fraying that partnership between us. It risks further instability in Northern Ireland and damage to key sectors of the economy.”

He said Ireland as a nation had adapted to Brexit but the row over the protocol was preventing Anglo-Irish relations from flourishing in other areas, including shared wind energy projects and education.

“We need to broaden out our relationship. The protocol got in the way of a revamp, reset of relations post-Brexit,” he said.

“I want to work in an open and constructive way with the new British prime minister.

“I sincerely believe that the EU would respond positively to a serious and genuine signal from the new British prime minister that their priority is to reach an agreed outcome on the issues around implementation of the protocol.”