His Sinn Fein party warned it could review its support for police in the British province, where thousands of people died during decades of Catholic-Protestant unrest.
The government rejected accusations that the arrest of Adams, the public face of the republican movement, was politically motivated.
Adams, 65, presented himself at a police station late Wednesday and was arrested for questioning over the murder of Jean McConville, a widowed mother of 10, in 1972.
McConville's children watched as she was dragged screaming from their home after the IRA accused her of being an informer. She was later found shot in the back of the head.
Detectives were today granted an extra 48 hours until tomorrow night to question Adams, after the previous deadline to charge or release him expired, the Police Service of Northern Ireland (PSNI) said.
Deputy First Minister Martin McGuinness, the top Sinn Fein figure in the power-sharing government in Belfast, had warned yesterday that the party would "reflect" on its cooperation with the police if Adams was charged.
Sinn Fein assembly member Alex Maskey told the BBC today the party would "monitor and review" its relationship with law enforcement services.
He said there was a "small element of people involved in policing who are politically motivated". The arrest came weeks before local and European elections.
"The people that I represent are scathing in their anger at the moment about the PSNI — and it's not just about in relation to Gerry Adams," he said.
Republican support for the reformed Police Service of Northern Ireland (PSNI) — which replaced the widely criticised Royal Ulster Constabulary (RUC) — was a key part of the peace process launched by the 1998 Good Friday agreement.
Sinn Fein, the political wing of the now-defunct IRA, wants Northern Ireland to leave the United Kingdom and join the Republic of Ireland to the south. Adams played a leading role in the Northern Ireland peace process.