Nine Independent TDs said Alan Shatter's position as Justice Minister is no longer tenable.
The group includes Shane Ross, Mattie McGrath, Catherine Murphy, John Halligan and Roisin Shortall, and they claim Minister Shatter's political judgment has been called into question recently.
"My position is that not only have I lost confidence in the Minister, but in recent days, from talking to the general public, they've lost confidence," said Deputy Finian McGrath.
"What I'm really concerned about is that the justice system in this country is being severely damaged.
"It needs to be dealt with head-on, and I think Shatter should go."
Joan Burton put her support and the support of the Government behind Shatter during Leader's Questions this morning.