The Prime Minister has come under fresh cross-party pressure in the Lords to intervene personally and try to break the deadlock in restoring a powersharing executive for Northern Ireland.
Former Northern Ireland secretary Lord Murphy of Torfaen said every previous successful agreement had been achieved by the direct involvement of the Prime Minister and the Irish Taoiseach.
The Labour peer said: "Isn't it about time the Prime Minister actually goes to Belfast and talks directly with the parties and the Irish Government?
"Until that happens, I fear we will make little progress," he warned at question time.
Government spokesman Viscount Younger of Leckie assured peers that Mrs May was taking "a very close interest" and had "close involvement" in the talks.
"Should she see fit, she will indeed travel to Northern Ireland," he said.
It hadn't always been the case in the past that the involvement of the Prime Minister had quickly led to agreement.
Tory Lord Cormack said the Prime Minister clearly had a close interest in the talks to achieve a powersharing deal, but added: "There is no substitute for a visit."
He urged her to go to Northern Ireland and "talk on the spot" with the various political parties involved.
Lord Younger said the Prime Minister would go "when she thinks it is right to do so" and when it would "make a material difference".
Lord Younger said the Government's priority remained to restore an inclusive powersharing executive, which was in the best interests of Northern Ireland.
He said ministers were determined that intensive negotiations should resume as soon as possible and stood ready to continue working with the parties.
Tory Lord Lexden asked whether, after "10 weeks of aborted talking", there was any prospect of a breakthrough and what contingency plans the Government had.
Lord Younger said "gaps" remained between the parties involved in the talks, but added: "We remain convinced they can be bridged."
He said ministers would do all they could to achieve a successful outcome.
"The deadline has now passed and the Secretary of State is under a duty to set a date for a new election. He will continue to keep that duty under review," he said.
Labour former minister Baroness Armstrong of Hill Top said if the Government was so busy with other issues such as Brexit, it might be time to appoint an independent person to do the "heavy-duty work" to keep the momentum going and resolve the deadlock.
Lord Younger said there was "heavy-duty work" going on to restore the powersharing executive with the Prime Minister keeping in continuous contact with the issues.
Labour spokesman Lord McAvoy also called for Mrs May to intervene. Lord Younger assured him she was "fully engaged and fully involved" with the issues and had met with the main parties in recent weeks