James Brokenshire has said there is still time to save powersharing in Stormont.
The Northern Ireland Secretary of State said there are only a small number of differences between Sinn Fein and the Democratic Unionists, mainly around Irish language rights, culture, identity and respect.
But the DUP MP Jeffrey Donaldson insisted that the Armed Forces Covenant, which aims to give ex-servicemen and women some priority medical treatment, housing assistance and school places for children, was integral to a deal.
"There will be no outcome that will not see that Armed Forces Covenant providing for the servicemen and women and the veterans and their families from Northern Ireland who have served this country," he said.
Mr Brokenshire said the Government wanted to see the ex-soldiers' benefits "touch" all parts of the UK.
The DUP and Sinn Fein failed to meet Mr Brokenshire's original Monday deadline for a deal, after Stormont had been effectively in limbo since January.
The crisis sparked a phone call between Prime Minister Theresa May and Irish Taoiseach Leo Varadkar yesterday while he was on a trade mission to the US west coast.
"They talked about the responsibility on parties to overcome their differences and the need for them to compromise on the outstanding issues for the benefit of all communities in Northern Ireland," Mrs May's official spokesman said.
In his statement to the House of Commons, the Secretary of State said he was making plans to impose a budget to protect public services over the next year but added that he would not be making the spending decisions.
He also said the Conservatives remained committed to the £1 billion investment, agreed in return for DUP votes in Westminster for Theresa May's minority Government.
"This Government, we stand by our commitments, and as a party we stand by the agreement that has been reached with the DUP. Nothing I have said today changes that," he said.
Mr Brokenshire warned that Northern Ireland will begin to run out of money in the coming weeks and said it is highly unlikely a new executive could be formed in time to pass a budget by the end of November.
But he added: "Even now - however unlikely this may be - should the parties demonstrate that an executive could be formed in the immediate future I would clearly wish to proceed instead with legislation to allow that to happen."
Mr Brokenshire said a last-minute powersharing deal would be conditional on a budget being agreed and passed by the end of November.
He also said he will reflect carefully on MLAs' salaries - £49,500 a year - which cannot be stalled or docked without primary legislation in Westminster.
Amid calls from the Alliance deputy leader Stephen Farry and others for a mediator to support the talks, Mr Brokenshire said the Government was considering other interventions and other ways to broker a deal.
But he added: "I think it still remains possible but it is certainly difficult.
"We will continue to keep a range of options available to us to see how we can move this process forward."
Mr Brokenshire told MPs he believed the best way forward for dealing with legacy allegations against former servicemen and women for incidents during the Troubles had been agreed at previous talks.
He said: "I want to move forward with a consultation around the Stormont House Agreement which sets out new institutions, new bodies that are very firmly intended to be balanced, proportionate, transparent, fair and equitable and thereby ensuring that soldiers are not unfairly treated."