Samaritan’s Purse has treated 130 patients in the 68-bed Central Park hospital since it opened on April 1, the group said on Tuesday. But its role in the response to the virus in New York has been criticized because of its position on L.G.B.T. issues and the past statements and political activities of Mr. Graham, a vocal supporter of President Trump.

On Sunday, Mr. Graham delivered an Easter message on Fox News while standing in front of his group’s medical tents in Central Park. In the message, which included footage of virus patients with their faces obscured, he described the pandemic in terms similar to those used by the president: “a storm” that “none of us anticipated” and “nobody expected.”

On Tuesday, Mr. Graham said that critics had been harassing Samaritan’s Purse with information requests while it was busy trying to save lives. He specifically mentioned the New York City Commission on Human Rights; the Reclaim Pride Coalition, a progressive L.G.B.T. group; and Democratic members of Congress.

“If any of these groups had funded and erected their own emergency field hospitals to serve Covid-19 patients in Central Park, we would join what we believe would be most New Yorkers — and Americans — in applauding and praying for them, not harassing them,” he wrote on Facebook.

Last week, four Democratic members of New York’s congressional delegation sent a letter to Kenneth L. Davis, the president of Mount Sinai Health System, Mayor Bill de Blasio and Gov. Andrew M. Cuomo asking how the Samaritan’s Purse field hospital would operate. The lawmakers also asked how the group came to be involved in the virus response in New York.