Some gay couples have loving, stable and monogamous relationships of "stunning" quality, the Archbishop of Canterbury has acknowledged.
The Most Reverend Justin Welby told the BBC he had "particular friends where I recognise that and am deeply challenged by it".
But he said he still supported the Church of England's formal opposition to active homosexuality.
He spoke ahead of his enthronement at Canterbury Cathedral, due at 15:00 GMT.
More than 50 protesters opposed to cuts to public services and changes to housing benefits, labelled the "bedroom tax" by Labour, have gathered outside the cathedral.
Police were monitoring the protest as the cathedral prepared to host 2,000 guests, including religious leaders, Prime Minister David Cameron, and the Prince of Wales and Duchess of Cornwall.
Campaigners, who have dubbed the protest a "Carnival Against the Cuts", waved placards including "Cuts are crippling me" and "Fight the bedroom tax".
Keith Woods, of Keep Our NHS Public, said: "This isn't a protest against royalty or the church because Justin Welby has been a supporter of what we are fighting for. But we couldn't let this occasion pass with David Cameron being here without saying we don't agree to the cuts that are hitting the poorest in society."
In his interview with the BBC, Archbishop Welby - the 105th Archbishop of Canterbury and spiritual leader of the Anglican communion - said: "You see gay relationships that are just stunning in the quality of the relationship."
While he said he did not doubt the Church's policy on same-sex relationships, he was "challenged as to how we respond to it".
"The Church of England holds very firmly, and continues to hold to the view, that marriage is a lifelong union of one man to one woman," he said.
"At the same time, at the heart of our understanding of what it is to be human, is the essential dignity of the human being. And so we have to be very clear about homophobia."
Asked if the Church would turn a blind eye to some gay relationships, he said: "It's not a blind eye - it's about loving people as they are and where they are.
"You'll find that in every church and you'll find that because it imitates the character and the practice of Jesus himself."
Pope Francis, whose inauguration Mass was on Tuesday, sent a goodwill message to Archbishop Welby ahead of his enthronement.
"Please be assured of my prayers as you take up your new responsibilities, and I ask you to pray for me as I respond to the new call that the Lord has addressed to me," said Pope Francis.
"I look forward to meeting you in the near future, and to continuing the warm fraternal relations that our predecessors enjoyed."
The Dean of Canterbury, Dr Robert Willis, said Archbishop Welby had already made a good impression.
"I think he will bring an enormous clarity and a sort of simplicity of trying to get to the heart of issues and already there is a willingness to have ordinary conversations with folk here," he said.
Ahead of his enthronement, Archbishop Welby went for an early-morning jog in the vicinity of Canterbury Cathedral.
He also tweeted: "Out early this morning, Canterbury is beautiful, human scale and history falling out of the walls everywhere. Grateful to be here."
Meanwhile, the Times has reported that the archbishop has offered to meet the gay rights campaigner Peter Tatchell after he criticised him in an open letter.
The newspaper said Archbishop Welby sent an email in which he thanked him for his "very thoughtful" letter, saying he would like to discuss it "without the mediation of the press".
Last month, the archbishop said he stood by the Church of England's opposition to the introduction of gay marriage.
He spoke before the Commons approved same-sex marriage in England and Wales by voting for the Marriage (Same Sex Couples) Bill, by a majority of 225.
The government believes the wording of the bill will ensure the Church of England and the Church in Wales will not face any legal challenges to their opposition to holding same-sex marriages in their buildings.
All religious organisations will be able to opt in to holding ceremonies, but the Church of England and the Church in Wales would first need to agree to change canon law.
Archbishop Welby, 57, is married with five children. He went to school at Eton, and later Cambridge University.
He rose to the top of the oil industry - ending up as treasurer of Enterprise Oil - and gave up a six-figure salary to train as a priest.
He was a vicar in Warwickshire, a canon of Coventry Cathedral, and the Dean of Liverpool, before being appointed as Bishop of Durham in November 2011.
The BBC's religious affairs correspondent, Robert Pigott, says the new archbishop is inheriting a Church which has seen congregation numbers decline dramatically in recent decades, and which is struggling to promote a Christian message to an increasingly sceptical and secular society.
It will be seen as his job to unite a Church deeply riven by disputes about women bishops, and, more dangerously, sexuality, our correspondent adds.