Westminster would be forced to pass a budget for Northern Ireland if Sinn Fein and the Democratic Unionist Party (DUP) fail to broker a power-sharing deal, James Brokenshire told MPs on Monday 3 July.
The Northern Ireland Secretary's statement to the House of Commons came after DUP leader Arlene Foster accused her republican rivals of making a "shopping list" of demands.
The talks are crucial since the 1998 Good Friday Agreement, an integral part of the peace process in the province, states that both parties must share power at Stormont, Northern Ireland's devolved assembly.
"If no agreement is reached, legislation in Westminster may then be required to give the authority for the expenditure of Northern Ireland departments for an Appropriations Bill," Brokenshire said.
"From my conversations with the head of the Northern Ireland civil service, we have not quite reached that critical point yet.
"But that point is coming and the lack of a formal budget is not something that can be sustained indefinitely. Similarly, decisions on capital expenditure and infrastructure and public services reforms and key sectors such as the health service, cannot be deferred for much longer."
The senior Conservative informed MPs that there had been progress in the negotiations. "I continue to believe that a deal remains achievable and, if an agreement is reached, I will bring forward legislation to enable an executive to be formed, possibly as earliest as this week," he said.
The political crisis in Northern Ireland erupted in January when Sinn Fein's Martin McGuinness, the former deputy first minister, quit his post in protest over the botched Renewable Heat Incentive (RHI).
McGuinness passed away in March and Sinn Fein have refused to appoint a new deputy first minister. The post-general election "confidence and supply" deal between the Conservatives and the DUP, so that May could continue to govern with a minority government, have added a big complication to the talks.
The DUP were able to secure £1bn for Northern Ireland as part of the agreement, but former Conservative Prime Minister Sir John Major has warned that the deal could damage the "fragile" peace process in the province.
"I am concerned about the deal. I am wary about it. I am dubious about it. Both for peace process reasons, but also for other reasons as well," the Tory grandee told BBC Radio 4's World at One show in June.