Some Roman Catholics argue that the first council of Nicea proves the Bishop of Rome was a universal bishop over all regions.
The ancient customs of Egypt, Libya and Pentapolis shall be maintained, according to which the bishop of Alexandria has authority over all these places since a similar custom exists with reference to the bishop of Rome. Similarly in Antioch and the other provinces the prerogatives of the churches are to be preserved. In general the following principle is evident: if anyone is made bishop without the consent of the metropolitan, this great synod determines that such a one shall not be a bishop. If however two or three by reason of personal rivalry dissent from the common vote of all, provided it is reasonable and in accordance with the church's canon, the vote of the majority shall prevail. (link)
The statement is ambiguous if the bishop of Rome is over the surrounding provence of Rome or over everything. However, it's important to note that Rufinus understood and translated the council as saying the bishop of Rome was over the Roman suburbs.
VI. The ancient custom in Alexandria and the city of Rome is to be maintained whereby [the bishop of the former] has charge of Egypt, while [the bishop of the latter] has charge of the suburbicarian churches. Rufinus (c340 to 410)