In a guest article for the US Catholic magazine "National Catholic Reporter" (Wednesday), Cruz explained that Dolan had claimed in New York Cathedral on 24 February that Pope Francis was in a very poor state of health and was "probably close to death".
Dolan's comment came one day after the Pope was diagnosed with a slight reduction in kidney function.
According to Cruz, however, such statements by a high-ranking church representative could "easily be misunderstood".
At the same time, the Chilean criticised a memo that Dolan had sent out a few days earlier via his vicar general to priests and employees of the Archdiocese of New York in preparation for the Pope's death.
In it, the cardinal had called the pope by his civil name, as those who do not recognise him do - and claimed that he was approaching the end of his earthly life. "This is blatant disrespect," said Cruz.
Church needs Francis
The Chilean also emphasised that the Church and the world need Pope Francis.
The 88-year-old does not have an easy illness.
"But I remain deeply optimistic that I will soon see him back in the Vatican," said the activist. He himself is looking forward to the reunion: "He will probably make a joke about it and tell me how much he has been touched by the countless prayers and messages he has received."
Cruz went on to say that his friends, his family and many other people he knows have never felt more welcome in the Church than after Francis' message that the Church is for everyone. "This message describes him perfectly," says Cruz.
And: "While some want to build a world of intolerance, Pope Francis has something much bigger in mind: a Church that embraces, heals and welcomes."