Peter Robinson has asked David Cameron to cage two former IRA prisoners, suspend the Assembly and help him create an opposition at Stormont as the political crisis grows.
The First Minister has also backed calls for independent monitoring of the IRA and urged the Government to convene urgent talks.
The two former republican prisoners were named by the DUP as Sean Kelly (43) from Ardoyne and Mark McDowell (47) from Short Strand.
Both were released early under the Good Friday Agreement but recently arrested as part of the investigation into the murder of former IRA man Kevin McGuigan. Both were subsequently released without charge.
Mr Robinson told the Belfast Telegraph: "If people are in breach of their licence agreements they should be returned to jail. There is no question about that at all. We will be able to give the Prime Minister at least two examples where that has occurred."
Jailing the two men is seen as a way of testing Sinn Fein's sincerity. If they mounted a campaign against it or walked away from the Executive, it would be presented by unionists as signs of sympathy with violence.
Another DUP demand - the suspension of the Assembly to allow talks to take place - is also controversial, though Taoiseach Enda Kenny said yesterday he thought it might happen. Earlier yesterday, a DUP bid to adjourn the Assembly was blocked at Stormont's business committee.
Speaking after his meeting with the Prime Minister, Mr Robinson said: "The government could suspend and we've asked the Prime Minister to consider that, if indeed the parties don't recognise an adjournment would be a better option."
He added: "Our concern is that the process requires urgent talks, the Prime Minister and Secretary of State (Theresa Villiers) agreed with that analysis.
"Our view was that those talks should be held in an atmosphere where people were concentrating on those issues and normal business was not proceeding."
Mr Robinson said decisions need to be made by Monday on how to clear space for talks.
Asked about independent monitoring of the IRA, he said: "I see that as being a small part of the issue of how to deal with paramilitary organisations. It is, on its own, not sufficient."
In a statement afterwards, No 10 said: "The prime minister recognised the gravity of the current situation and the need to rebuild trust and confidence in the political process in Northern Ireland."
The PM has asked Ms Villiers to hold further talks with the aim of agreeing a way forward, the statement said.
Police believe the killing of Mr McGuigan in east Belfast was a revenge attack by republican associates of IRA commander Gerard 'Jock' Davison, who was gunned down in May.
Chief Constable George Hamilton has said the Provisional IRA still exists and some members were involved in the murder of father-of-nine Mr McGuigan last month.
Sinn Fein Deputy First Minister Martin McGuinness opposes any suspension of Stormont and claimed "the appalling murders of Jock Davison and Kevin McGuigan which were carried out by criminals are now being exploited by unionists for narrow political self-interest".
He said he would be willing to take part in a new talks process.
"I don't think it was a good idea looking for a suspension of the institutions for a four-week period and I think it would be an even worse idea if David Cameron were to effectively suspend these institutions and return direct rule ministers for whatever time," he said.
Despite the differences between parties, there is consensus over talks going ahead. The talks will have to encompass the Stormont House Agreement, concluded last Christmas but never implemented.
In Dublin, Ms Villiers and Irish Foreign Minister Charlie Flanagan gave their backing to another DUP proposal which is supported by the UUP - the creation of a new monitoring body to report on the state of the paramilitary ceasefires and criminal activity by groups connected to political parties.
Ms Villiers said bringing back ceasefire monitors could restore trust between unionists and republicans.
Secretary of State Theresa Villiers has powers to return a prisoner to jail to finish their sentence if they have been released on licence and are suspected of re-offending.
There does not have to be proof beyond reasonable doubt.
This has happened to Sean Kelly before. He was jailed for life for his part in the IRA's 1993 Shankill bombing which killed nine people. He served seven years before being released but in July 2005 his licence was revoked by the then Northern Ireland Secretary Peter Hain on suspicion of shooting a man.
He was released less than a fortnight later in return for a statement from the IRA that they were ending all criminality and terrorism. Peter Robinson argued that this undertaking had not been kept. At the time Sinn Fein protested the imprisonment and called it destabilising.
The other ex-prisoner the DUP believes should have his licence revoked is Mark McDowell. He was sentenced to 14 years in December 1997 for possession of firearms.
Peter Robinson had been hoping the UUP would support his party's call for the Assembly to be suspended for four weeks, perhaps six, to allow for talks. The fact that the UUP didn't shows the depth of the grudge match between the two former allies.
Stormont's Deputy First Minister said he would be prepared to take part in a new talks process, but cautioned against any suspension of the political institutions.