The world's most prominent gay bishop  has written an open letter to Pope Francis after the Vatican signalled that it was unhappy with some of those invited to a star-studded White House party being thrown for the Pope this week by President Barack Obama.

Bishop Gene Robinson, former Bishop of New Hampshire, said he knew he would not be the first gay bishop the Pope had met, as some "undoubtedly" work with and for Pope Francis in the Vatican.

Pope Francis leaves Cuba on Tuesday for Washington, where the gay, twice-married and now twice-divorced former Bishop of New Hampshire  is among those invited to a celebration party. The Vatican is understod to have disputed the guest list, which as well as Bishop Robinson, a father of two who divorced his wife in 1986 and his husband last year, includes an activist nun and some transgender campaigners. They are among 15,000 guests who will assemble on the lawn of the White House on Wednesday morning.

The Wall Street Journal reported: "The tension exemplifies concerns among conservative Catholics, including many bishops, that the White House will use the pope's visit to play down its differences with church leaders on such contentious issues as same-sex marriage and the contraception mandate in the health care law."

The election of Bishop Robinson, who retired in 2013, as Bishop of New Hampshire in the US Episcopal Church, was among the events that triggered the crisis that engulfed the Anglican Communion. Archbishop of Canterbury Justin Welby has summoned the 37 other Primates from the separate provinces to a meeting in January to debate whether a loosening of ties towards a federal model might be a way forward to preserve unity.

Pope Francis surprised journalists on a flight home from World Youth Day in Rio in 2013 when he said: "If a person is gay and seeks God and has good will, who am I to judge him?" The issue will be on the table at next month's Synod on the Family and despite his apparent personal sympathies, the Pope appears unlikely to waver from traditional church doctrine on this or other issues such as marriage after divorce.

In his open letter to Pope Francis, Bishop Gene said:  "I pray for you every day, because your pastoral responsibility is so daunting, and even if you are Pope, you are still only human."

Bishop Robinson lamented that Sister Simone Campbell, one of the nuns working day in and day out on behalf of the poor, "is lumped in with me as a purported offence to you".

Bishop Gene described the Pope as "saintly" and said he suspected the objection did not represent his own views but the views of those who wish to "protect" him from the world.

"I suppose the Vatican official's concern has to do with my having been elected and consecrated a Bishop of The Episcopal Church, while at the same time being an openly gay, partnered man. Were I ever to have the honor of meeting you, I would of course not be the first gay man or gay bishop with whom you have had contact. Some of them, undoubtedly, work with and for you in the Vatican. Based on your demonstrated and notorious compassion, I suspect you will not be offended by a gay bishop and a feisty nun somewhere in the crowd of 10,000 admirers."

He added: "We disagree in our understandings about sexuality and the diverse and wonderful ways God has made us. But as far as I am concerned, that does not keep me from admiring you and praying for you and your ministry."

He said they had so much in common, such as a concern for the marginalised. "It seems that in these times, the greatest sin would be to write one another off and to stop caring about one another."

Bishop Gene, now a senior fellow at the Center for American Progress, added: "Something tells me that you will not be offended if I am somewhere in the crowd of 10,000, gathered to welcome you to America, with respect and wholehearted affection. And I doubt that you need your colleagues in the Vatican to be so protective of you."