“I see this as an opportunity to allow an American natural resource to help bolster both countries’ economies,” he said. “The overall goal of the Trump administration is to sell what Americans make to bolster this economy. If you are selling it to a partner, a neighbor, even better.”

Mr. Perry said his stance was not clouded by his former job on the board of Energy Transfer. Having already passed through the revolving door between government and the energy industry, Mr. Perry said, he was in no way conflicted about his new role.

“I work for Donald Trump and I work for the American people,” he said.

Mr. Trump’s threats against Mexico and shifting statements about withdrawing from Nafta have prompted some worry, however, persuading Mexican officials to begin exploring options in the event of a cutoff.

“In the context of an escalating trade war, a cutoff of gas by one side or the other is possible,” said Kevin Book, managing director of ClearView Energy Partners, an energy research firm.

Such a move, according to Mr. Book, would summon what he calls a “mutually assured destruction scenario,” in which American companies suffer a serious loss of income and Mexico faces an energy shortage that could devastate the most basic functions of its capital, Mexico City.

The impact on the United States could also hit home for some of the most important members of Mr. Trump’s cabinet and support base. With American gas exports to Mexico expected to double by 2019, most gas will come from Texas, a vital Republican stronghold that is the home state of both Mr. Perry and Secretary of State Rex W. Tillerson.

Mr. Trump’s threats have “created some worry on Mexico’s part, and as a result Mexico has looked at its backups and alternatives,” said Carlos Pascual, the former American ambassador to Mexico and a senior vice president for IHS Global Energy. “But the first screams that would go up if the U.S. were to cut off natural gas shipments to Mexico would come from the oil and gas producers in Texas.”