Those involved in the attack on a Liverpool fan before Tuesday's Champions League semi-final have "brought shame" on Roma, the Italian club said.
Reports of violence outside Anfield emerged just before kick-off of the first leg which Liverpool went on to win 5-2.
Merseyside Police initially confirmed they were investigating the "serious assault" of a man outside The Albert pub on Walton Breck Road near the stadium, with the victim a 53-year-old who suffered serious head injuries.
Police later announced two arrests had been made on suspicion of attempted murder, with two men from Rome, aged 25 and 26, taken into custody.
The Liverpool fan remains in a critical condition on Wednesday and Roma have released a statement, speaking of the ignominy that has been brought upon their club.
Their statement read: "Roma condemns in the strongest possible terms the abhorrent behaviour of a small minority of travelling fans who brought shame on the club and the vast majority of Roma's well-behaved supporters at Anfield after getting involved in clashes with Liverpool supporters before last night's [Tuesday] fixture.
"There is no place for this type of vile behaviour in football and the club is now cooperating with Liverpool Football Club, UEFA and the authorities.
"The club's thoughts and prayers are with the 53-year-old Liverpool fan in hospital and his family at this time."
