Sinn Fein president Gerry Adams has said his party will not be deflected from "doing the right thing", even if members' lives are under threat.
Gerry Adams said his party would not be deflected by threats
Republican sources said threats to senior Sinn Fein members have come from disaffected IRA members who left the organisation in recent months.
They are said to be opposed to the party supporting the police.
Gerry Adams, Martin McGuinness and Gerry Kelly have now increased their security, the sources claimed.
Sinn Fein will have to back the police as part of any deal to restore devolution.
The party is said to be concerned that the disaffected IRA members could join the main dissident groups, the Real and Continuity IRA, which have both branded the Sinn Fein leadership as traitors.
Police have warned recently about the possibility of attacks by dissident reopublicans to try to derail efforts to restore the Northern Ireland devolution.
Mr Adams said party members would continue to work to achieve progress despite the threats.
"I won't allow it, and none of us will allow it, to deflect ourselves from continuing the work we were elected to do," he said.
"This is disturbing for our families and for those who are close to us. But we have a task to do and we will prevail."
'Nothing to offer'
Northern Ireland Secretary Peter Hain said those who made the threats had nothing to offer society.
"We have seen fire bomb attacks and other incidents and threats of this kind," he said.
"Those committed to the path of stability, peace and democracy as the Sinn Fein leaders are - and as they have shown they are determined to be to take Northern Ireland into permanent stability with peace locked in - are obviously, like the rest of us, the targets for dissidents."
However, the DUP's Ian Paisley Junior expressed scepticism about the threats.
"Sinn Fein's latest gambit for public sympathy that they are under threat from dissident republicans is nothing more than a pathetic distraction to prevent Sinn Fein from supporting the police," he said on Monday.
"The fact is Sinn Fein, despite all their talk, have done nothing to encourage public support for policing, hence their present difficulties."