The Democratic Unionists have been defeated in a bid for a four-week adjournment of the Northern Ireland Assembly to allow for political negotiations, a party spokesman said.
The Ulster Unionists have decided to leave the devolved powersharing ministerial Executive after police said the IRA still exists.
The largest party, the DUP, had called for Assembly meetings which are due to begin next week to be stalled during crisis talks but was overruled by the other parties.
DUP leader Peter Robinson is due to meet Prime Minister David Cameron in London later.
Police Service of Northern Ireland (PSNI) chief constable George Hamilton has said the Provisional IRA still exists and some members, along with a group styling itself Action Against Drugs, were involved in the murder of a father-of-nine last month.
A DUP spokesman said: ``We have sought to extend the Assembly recess, to not return until October. That was not successful.''
Mr Cameron is expected to come under pressure to penalise Sinn Fein when he meets Mr Robinson and his DUP deputy Nigel Dodds at Downing Street today.
Mr Cameron’s official spokeswoman said the Downing Street meeting with Mr Robinson was “an opportunity for both of them to discuss the latest political situation in Northern Ireland and how we can continue to move forward”.
The PM’s spokeswoman added: “We are clear we want to work with parties there to implement the Stormont House Agreement.”
The political fallout following the murder of IRA man Kevin McGuigan will also top the agenda in Dublin where Northern Ireland Secretary Theresa Villiers will sit down with Foreign Affairs Minister Charlie Flanagan and Justice Minister Frances Fitzgerald, who has asked Garda chiefs to review Provisional IRA (PIRA) activity.
The controversy was sparked when the chief constable said the PIRA still exists and some members, along with a group styling itself Action Against Drugs, were involved in the murder of Mr McGuigan. Police believe the killing was a revenge attack by republican associates of IRA commander Gerard ’Jock’ Davison who was gunned down in May.
The chief constable said the PIRA is not engaged in terrorism – instead pursuing peaceful, political republicanism – and that there is no evidence the McGuigan killing was sanctioned by the IRA leadership.
Taoiseach Enda Kenny insisted that Sinn Féin's stance of calling on people to come forward with information on law breaking was not sufficient.
"It's not satisfactory for me, merely to be calling on anybody out there who knows anything about these things to be coming forward," he said.
"Obviously those who were involved in those years know many names, and they should be in contact with those names so that the law of the land can apply and that people in many areas, on the border in particular, are not frightened or terrified to open their mouths."
Sinn Féin leader Gerry Adams TD has responded, saying: "The Taoiseach needs to resist the temptation to play politics with the brutal murders of Jock Davison and Kevin McGuigan in Belfast.
"These are very clearly matters for the criminal justice system and the PSNI should be allowed to pursue their investigations without political interference.
"The IRA is gone away and Mr Kenny knows that full well. The Taoiseach needs to reflect on his responsibilities to the peace and political processes and should refrain from such offensive and vindictive interventions."
The Ulster Unionist Party (UUP) has said it could no longer work with Sinn Féin because trust has been shattered.
On Saturday it unanimously voted to leave the power-sharing Executive and the party’s only minister, Danny Kennedy, is due to resign today.
Although the move is not enough to collapse the Executive it has put pressure on the DUP.
Mr Robinson, who has been on holiday, branded the UUP decision irrational, illogical and based on “political expediency” rather than principle.
Walking away should be a last resort, he said.
Meanwhile, Sinn Féin said it would not be “deflected” and accused political opponents of exploiting murder.
Conor Murphy, MLA for Newry and Armagh, said: “We and the 178,000 people who voted for us in the last Assembly elections will not be excluded or discriminated against. Those days are over.”