The British and Irish governments have welcomed news that Sinn Fein will hold a special conference next month to discuss signing up to policing.
Policing has been a dividing issue between the DUP and Sinn Fein
Downing Street said there was now a real prospect of all NI parties and communities supporting the rule of law.
Speaking after talks in Dublin on Friday, Gerry Adams said the meeting would be held if the two governments and the DUP gave a positive response.
The move has also been welcomed by Taoiseach Bertie Ahern.
Mr Ahern welcomed the Sinn Fein executive's "landmark and timely decision".
He said: "Sinn Fein has taken an important step on the road to support for policing in Northern Ireland."
A Downing Street spokesman said there was now, for the first time, "the real prospect of all parties and all sections of the community in Northern Ireland supporting the rule of law in Northern Ireland".
"This statement is significant because of the unequivocal support that Sinn Fein says it will offer - if this motion is passed at the ard fheis - to not just the police but also to those in communities who report crimes to the police," the spokesman added.
Sinn Fein support for policing would be viewed as removing one of the main obstacles to restoring devolution.
More than two-thirds of the executive voted in favour of the meeting.
The party has historically opposed recognising the Police Service of Northern Ireland (PSNI) and its predecessor the Royal Ulster Constabulary (RUC), because of what it sees as a Protestant bias within the service.
The DUP - the largest party in Northern Ireland - has previously refused to speak to Sinn Fein until it recognises and accepts the PSNI.
Speaking after the Sinn Fein vote on Friday evening, DUP deputy leader Peter Robinson said it would be "churlish not to acknowledge the potential" of the steps taken by the republicans.
But he warned that unionists would have to study Sinn Fein's words and actions carefully.
A date for the Sinn Fein conference, or ard fheis, has not yet been confirmed.
Speaking after the six-hour meeting of the executive, Mr Adams said the debate was "frank, comradely and robust".
"I put a motion to the party leadership and the party leadership endorsed that by more than the two thirds majority," he said.
Mr Adams said he would now be engaged in efforts to deal with concerns among republicans over the proposals.
"I am totally wedded to the idea of every single person who wants to be part of this debate, being part of the debate, because it's about the future, it's about the type of Ireland we want to see."
Sinn Fein said the motion put forward would include a commitment to "actively encourage everyone in the community to co-operate fully with the police services in tackling crime in all areas and actively supporting all the criminal justice institutions".
BBC Ireland correspondent Denis Murray said the key for the DUP would be "delivery".
Alex Attwood, SDLP spokesman, said: "Sinn Fein now appear to be backing out of the wrong position they've adopted on policing over the last number of years...
"Everybody including the DUP should now consider acting quickly and positively to the situation that's developing."
Ulster Unionist leader Sir Reg Empey said Sinn Fein had "lost the battle on policing".
Alliance Party leader David Ford said: "Some of us have been waiting for this since 1998. It's long overdue but nonetheless welcome."
The British and Irish governments have named 7 March as the date for fresh assembly elections, with a new executive expected to be up and running by 26 March.
Talks aimed at restoring the assembly and its executive have been taking place since the St Andrews Agreement negotiations in November.