Violent dissident republicans should disband, the Sinn Fein leader said.
Anti-peace process renegades threatened the party's vice president Michelle O'Neill and veteran policing spokesman Gerry Kelly after they supported a recent recruitment campaign for new Catholic officers.
Party president Mary-Lou McDonald said they would not be deterred or intimidated by the gunmen.
She added: "These people have no politics, no strategy and nothing to offer.
"They are at war with their community and are now threatening political representatives who serve the people."
The event was intended to encourage more Catholics to join the Police Service of Northern Ireland (PSNI).
Senior commanders have become concerned in recent years over a slide in the proportion of Catholic officers amid the severe threat posed by dissident republicans who try to kill members of the security forces.
The Sinn Fein president said: "Sinn Fein will not be deterred or intimidated.
"These groups have nothing to offer. It's time they packed up and disbanded."
Ms O'Neill and Mr Kelly's attendance at a PSNI recruitment event was hailed by Chief Constable Simon Byrne as "seismic and historic".
It was the first time such a senior Sinn Fein figure had attended such a meeting, although the party has expressed support for police in Northern Ireland on many occasions in the past.
Last year there were attempted bomb attacks by dissident republicans targeting police in Belfast, Craigavon in Co Armagh and near the Irish border in Fermanagh.
The New IRA and Continuity IRA are involved.
Police have branded as "cruel and disgusting" anti-PSNI recruitment posters depicting an officer who was severely injured in a bomb attack.
The posters used a picture of Peadar Heffron along with a warning that anyone thinking of joining the police could suffer similar injuries.
Mr Heffron lost a leg when a dissident bomb detonated under his car near Randalstown in 2010 as he travelled to work. He now uses a wheelchair.
Meanwhile, Ms McDonald commended her negotiating, Executive and Assembly teams - led by Ms O'Neill - for "working hard for citizens".
She listed recent successes following the restoration of devolved political powersharing at Stormont.
The party leader said: "Already in the Executive we have seen measures taken to tackle poverty, including moving quickly to end the nurses dispute of equal pay; extending welfare mitigations, a new house building programme has been announced.
"Additional funding has been made available for education and the victims and survivors of the contaminated blood scandal in the north will receive compensation payments."