Compassion International executives learned early last year, from an item in an Indian newspaper, that their group had been added to the list of organizations whose transfers required prior permission by the Ministry of Home Affairs, said Stephen Oakley, Compassion’s general counsel.

By summer, $600,000 in donations was stuck in an Indian bank account awaiting permission that did not come. In November, two of the group’s main affiliates — in Chennai and Kolkata — were denied authorization to use foreign funds.

In the United States, Mr. Mellado was pressing, with an increasing sense of urgency, for an opportunity to plead his case with Indian officials.

But the only interlocutors they could find were through unofficial channels. In October, a Washington-based representative of the R.S.S., Shekhar Tiwari, reached out to John Prabhudoss, who heads an umbrella organization of Indian-American Christians and has a long association with Compassion International and its leaders, Mr. Prabhudoss said.

Mr. Mellado said he was puzzled by the indirect outreach, but decided to give it a try.

“We are trying to navigate through understanding of the dynamics on the Indian side,” he said. “We understand that the B.J.P. and the R.S.S. are tied together somehow, so it seems to us that we also need to be talking to the R.S.S.”

Through Mr. Prabhudoss, Mr. Tiwari put forward a proposal: The government might view Compassion International more favorably if the charity routed a portion of its $45 million in annual charitable donations away from churches and through non-Christian aid groups, including Hindu ones.

“They were asking me, ‘How do you think we can solve this problem?’” Mr. Tiwari said. “I told them, instead of having all your partners Christian, have some Buddhists, Hindus, Jains, Sikh organizations.”