Police arrested Adams on Wednesday over the abduction and murder of Jean McConville, a killing he said he was "innocent of any part" in. They have until 1900 GMT to decide whether to charge, release him, or seek a further extension in custody.
His detention has raised tensions among Northern Ireland's power-sharing government and the province's fragile peace. First Minister Peter Robinson on Sunday accused Sinn Fein, his partner in government, of a "thuggish attempt to blackmail" police through its criticism of the arrest.
Nationalist Sinn Fein, which shares power with Robinson's Protestant Democratic Unionist Party (DUP), has said the arrest is a deliberate attempt by "dark forces" in the Police Service of Northern Ireland (PSNI) to undermine the peace process.
Deputy first minister Martin McGuinness stopped short of saying Sinn Fein would remove its support for the PSNI, a move that would spark a major crisis. But he said on Friday that it would wait to see if the situation was resolved satisfactorily.
"The publicly conveyed threat to the PSNI delivered by the highest levels of Sinn Fein that they will reassess their attitude to policing if Gerry Adams is charged is a despicable, thuggish attempt to blackmail the PSNI," Robinson said in a statement.
"The threat now means that ordinary decent citizens will conclude that the PSNI and the PPS (Public Prosecution Service) have succumbed to a crude and overt political threat if Adams is not charged.
"I warn Sinn Fein that they have crossed the line and should immediately cease this destructive behaviour."
Responding in Dublin, McGuinness said he unequivocally supported the PSNI but had a problem with a tiny number of people in influential positions opposed to Sinn Fein who saw the arrest of Adams as "payback time".
He added that the peace process was not at risk over the crisis, nor was the power-sharing government under threat from Sinn Fein. Northern Ireland Justice Minister David Ford urged both side to take a step back and let the police to their job.
NO SIGNS OF TROUBLE
Adams' arrest over the killing of McConville is among the most significant in Northern Ireland since a 1998 peace deal ended decades of tit-for-tat killings between Irish Catholic nationalists and mostly Protestant pro-British loyalists.
The Sinn Fein leader, who is a member of parliament in the Irish republic, has been dogged throughout his career by accusations from former IRA fighters that he was involved in its campaign of killings, a charge he has repeatedly denied.
Gerry Kelly, a Sinn Fein member of the Northern Ireland Assembly who on Sunday visited Adams and his legal team at the police station where he is being held, told reporters that Adams looked well and was being treated well by police.
Two dozen pro-British activists raised a union flag from a lamp post near the police station. However, there have been no signs of trouble across the province since Adams' arrest.
Kelly said that according to Adams' solicitor, the former leader of the IRA's political wing was being quizzed on decades- old photographs and newspaper articles, a tactic McGuinness described as a trawling exercise similar to the 1970s when attempts were made to charge Adams with IRA membership.
Unlike McGuinness, Adams, who helped broker a 1998 peace deal that largely ended three decades of sectarian violence, has always denied membership of the IRA.