Dr John Sentamu was welcomed to the York Mosque and Islamic Centre on Monday by Iman Abid Salik and local residents.
He said: "We each have a responsibility to foster better community relations and improve our sense of what it means to be a good neighbour."
The Archbishop went on to encourage people to follow the challenge made by Old Testament prophet Micah.
Dr Sentamu said: "[Micah] challenges his listeners to 'live justly, love mercy and walk humbly with your God' and so I am very much looking forward to visiting York Mosque today and to find out more of the social action projects that York Mosque is doing."
Among the ways UK Muslims are already trying to reach out to their local communities is through the yearly Visit My Mosque programme.
Last month, more than 700 people visited York mosque, which was among 150 mosques across the country opening their doors to people of all faiths.
Welcoming the Archbishop, Imam Salik said: "We recently held an open day and, on behalf of the whole congregation of York Mosque, we would like to express deep and sincere gratitude to each and every person who made it possible and to our neighbours and friends from York and beyond who came along to support the day. It was so humbling.
"Islam, like other faiths, places great emphasis on improving understanding between peoples of different backgrounds and traditions. We look forward to welcoming the Archbishop and will be holding more open days soon".