ROME (Reuters) -Italian police arrested a U.S. citizen on Friday in connection with the death of a woman and her baby daughter whose naked bodies were found in a park in central Rome.

The man, who was not named, was arrested on the Greek island of Skiathos, Rome's chief prosecutor Francesco Lo Voi told reporters at a news conference.

The case has grabbed headlines in Italy since the mother and her child, who was less than one year old, were found dead on Saturday in Villa Pamphili, Rome's largest central city park.

None of the people involved have been named, and prosecutors in the case told reporters they had still not been able to identify the mother or the child.

Italian newspapers have reported that the mother and child were also U.S. citizens, but prosecutors did not confirm this.

Lo Voi said the arrested man had declared he was the father of the child, and there was "robust evidence" that he had killed her, while the cause of death of the mother was less clear.

The suspect flew to Skiathos from Rome on Wednesday, and his DNA would be examined to establish whether he was the father, the prosecutor said.

He was arrested based on evidence including witness accounts and surveillance camera footage, while the fact he had flown to Greece shortly after being seen with the victims "in itself doesn't count in his favour," Lo Voi said.

Lead prosecutor Giuseppe Cascini said the man had been seen with the child in his arms after the presumed time of death of the mother.

The evidence against the suspect was particularly strong regarding the death of the child, Cascini said, but the case was "a probable dual murder".

The prosecutors thanked the U.S. FBI for its help in identifying the man, and the Greek authorities for their role in the arrest.

The man, woman and child were first seen together in Italy in April, and there was no record of any of them in the country before then, they said.

(Reporting by Paolo Chiriatti; Writing by Gavin Jones; Editing by Mark Porter and Aidan Lewis)