The senior republican said he hoped to build on the conciliatory “outreach” gesture in the time ahead.
MORE: Prince Charles shakes hands with Old Bailey bomber Gerry KellyThe party’s Belfast Lord Mayor Deirdre Hargey and former Culture Minister Caral Ni Chuilin also met Charles during an event in Belfast.
Stormont’s devolved administration has not sat for months in a row over identity which has polarised relations between Northern Ireland’s two largest parties, Sinn Fein and the Democratic Unionists.
Mr Kelly said: “Republicanism is built on interculture, especially north Belfast.
“We understand that in Ireland and in this part of Ireland we have people who are British and see themselves as British, and this is part of their culture as well.
“I would hope that there would be reciprocation, I am not demanding that, that is not why I came.
“If we can build on this, I don’t want to exaggerate this as if it is a huge thing.
“I want them (unionists) to understand that that is a part of outreach, it is not the only bit of outreach I have done, and in North Belfast there is outreach all the time, it does not get talked about at all.”
Former deputy first minister and Sinn Fein leader Martin McGuinness shook hands with the Queen when she came to Belfast six years ago.
Mr Kelly is a former IRA prisoner who has supported the peace process and helped defuse the violent stand-off over the Ardoyne loyal order parade, just a short distance from where he met Charles at Carlisle Memorial Church.
He said he had no difficulty shaking the heir to the throne’s hand.
“Martin McGuinness stepped out, he was the leader who did it, we are following in his footsteps.”
Mr Kelly added: “Ireland overall and the north especially is becoming an intercultural society, and if you want to pick a place for interculture then north Belfast, ironically, is the place to see it as well.”
The building where the encounter took place, Carlisle Memorial Church, was once known as the Methodist Cathedral, and Mr Kelly said he wanted to see it brought back into use.
The Ulster Orchestra entertained Charles during his visit and Mr Kelly said the Orchestra may be planning a residence, or going there more often.
He said: “It has been a good day.”