Justin Welby hosted a special meal at Lambeth Palace to mark Eid.
In his message, he remembered those celebrating the festival in areas of unrest around the world.
He said: "Our prayers are daily with those of all faiths who are menaced by war, by kidnap, by violence, by suffering, by poverty.
"That makes me appreciate all the more the way that in this country we do manage to work together, and are learning to live together, and to build a country of greater promise through our joint efforts together."
Archbishop Welby said he had come to treasure his friendship with a Muslim man as they shared each other's scriptures and discussed their faiths during Lent.
He acknowledged that there had been difficulties such as the recent so-called "Trojan Horse" affair at schools in Birmingham but stressed that Christians and Muslims needed to work together, not in opposition, in dealing with such issues.
He said Christians and Muslims needed to listen to each other as they worked out what it meant to be a 'community of communities' in this country: "To be a single community of loyalty to the country in which we live, to its values, to the wonderful things we get from it.
"But also to be in reality and with integrity, our own communities, enjoying all the richness that comes from our history." He said.
He added there was much to be learned and discussed and that Christians and Muslims needed to work hard together.