I exhort therefore, first of all, that petitions, prayers, intercessions, and givings of thanks, be made for all men:
This verse (1 Timothy 2:1) should answer the question of whether we should pray for the unsaved. "All men" certainly includes them. Paul undoubtedly meant all kinds of people rather than every single individual. The king at the time Paul wrote this epistle was Nero, an unbeliever for whom Paul specifically told his readers to pray. Furthermore the focus of their request was to be not only their own tranquillity but the king’s salvation (1 Timothy 2:4).