Secretary of State Julian Smith had told MLAs the Stormont Executive must return by next Monday if they want any influence over abortion reform in Northern Ireland.
An intensive phase of talks aiming to restore power-sharing at Stormont will take place later this week.
Mr Smith has announced that parties will be meeting on Thursday and Friday.
On Monday evening the Secretary of State said that he had met with DUP leader Arlene Foster.
"A busy week ahead working with all parties to get Stormont back up and running," he tweeted.
The talks will be the last opportunity for local parties to reach an agreement before Monday, October 21, when the UK Government will become obligated to legislate to introduce new abortion and same-sex marriage laws to Northern Ireland.
"The key message to parties in the talks is if you want to influence the abortion reform that has been set by Westminster we need to get movement this week," the Secretary of State told UTV.
"We need to get movement for decision-making across the board this week to help public services, help citizens in Northern Ireland get the decisions they need, but to shape that abortion law, reform that is best shaped in Northern Ireland, we need parties in talks this week and to be back in an Executive by next Monday."
Sunday marked 1000 days since Northern Ireland last had a functioning Assembly.
The institutions collapsed after the late deputy First Minister Martin McGuinness resigned in January 2017 over the RHI scandal and equality issues.
Talks to restore power-sharing have repeatedly failed and the current round, which began after the murder of journalist Lyra McKee in April, have stagnated.
The largest issue remains an Irish Language Act, with the DUP refusing to budge on what remains a red line for Sinn Fein.
Sinn Fein vice-President Michelle O'Neill said that the UK Government's stance on Brexit talks was impeding the restoration of Stormont.
“The British government’s proposal of a unionist veto in the Brexit context is totally unacceptable and makes political progress even more difficult," the Mid Ulster MLA said.
“In terms of attempts to restore the political institutions, let me be absolutely clear, there will be no unionist veto at Stormont in terms of the Brexit negotiations.
“If the institutions are to be re-established on a durable basis, the issues of equality, rights, integrity and respect which caused the collapse of the Assembly must also be addressed and resolved.”
SDLP leader Colum Eastwood again suggested reforming the petition of concern mechanism in an attempt to restore power-sharing.
A petition of concern can be used if at least 30 MLAs agree to support the measure.
Any legislation subject to a petition of concern will require at least 40% support from nationalist and unionist parties to be approved.
"The SDLP has made bold proposals for a fair reform of the petition of concern that, we believe, all parties can back that would allow the restoration of government in the short term," Foyle MLA Mr Eastwood said.
"We know there is an assembly majority for Irish language legislation, for marriage equality, for welfare mitigation and more. The only people who benefit from this stalemate are those who refuse to accept those measures.
“I feel the burden to restore government. I understand the pain and the stress people are feeling in our communities. But we must be clear – the SDLP and others are doing all we can to get an Executive back.
"The failure to compromise or to endorse the compromise we have proposed lies with the DUP and Sinn Fein. We have not been found wanting and will not be found wanting this week.
“It’s time to restore government and deliver for the people we represent."