A rejection of police support would see Northern Ireland's assembly dissolved on Tuesday and the province run indefinitely from London.
Protestant politicians want Sinn Fein to agree to support the police before they consider working with them again in the Belfast-based assembly, which was set up under a 1998 peace deal.
|The IRA's campaign is remembered on |
the walls of Belfast. [AP]
The party is the political wing of the Irish Republican Army (IRA) which killed nearly 300 police officers during a 30-year armed campaign against British rule.
Sinn Fein's policy on the police service has been to restore the assembly, which has been suspended since 2002 amid claims that a republican spy ring was operating there.
Republicans who largely favour union with the Republic of Ireland believe Northern Ireland's police force is biased in favour of Protestants.
Earlier this week, a police ombudsman's report revealed that police colluded with, and protected ,Protestant paramilitaries in the early 1990's.
Adams faced protesters and a media scrum as he arrived for the meeting at the Royal Dublin Society conference centre.
The demonstrators included members of Republican Sinn Fein, a separate party formed in 1986 after Sinn Fein ended its abstentionist policy in the Irish parliament in Dublin and Belfast.
Placards read "Yes to British withdrawal", "No British police, no British laws, no British courts acceptable in Ireland".
Adams acknowledged that not everyone within republicanism supported the change, but as part of their preparations for government, "reaching out to unionism" was vital, he said.