Patrick Manning urged Castro to visit whenever "he considers appropriate."
It was unclear if Castro would accept his offer, or if a trip could coincide with the Summit of the Americas on April 17.
Manning is visiting Cuba and met with Castro behind closed doors Sunday.
State media reported the meeting and the invitation to visit on Monday.
United States President Barack Obama and the leaders of 34 Western Hemisphere countries will attend the summit.
Cuba won't attend.
Manning has said he thinks Cuba will dominate the agenda and there will be agreement on how to incorporate the country back into hemispheric relations.
- AP stories