Eric Wohlschlegel, a spokesman for the American Petroleum Institute, said he could not comment on the letter because he had not seen it.

Allegations that contributions from donors like Mr. Koch influence institutions exhibits are not new. A 2010 investigation in The New Yorker noted that an underlying message of exhibits in the David H. Koch Hall of Human Origins at the Smithsonian National Museum of Natural History is that humans “evolved in response to a changing world.” The article said that such language suggests that climate change has been a feature of the planet since prehistoric times, which plays down human contributions to climate change.

Randall Kremer, director of public affairs for the museum, said that Mr. Koch served on the advisory board, which is “a consultative board not a governing board,” and that “the museum director has no plans to ask any members to step down.”

Mr. Kremer added that while Mr. Koch was the largest single donor to the museum, “he signed our standard gift agreement, which prohibits donor or sponsor involvement in content.”

A spokesman for the American Museum of Natural History, Roberto Lebron, said, “Donors do not determine the interpretation or presentation of scientific content.”

Eric Chivian, founder of the center for health and the global environment at Harvard Medical School and a signer of the letter, said he was not convinced that policies barring donors from having direct control over exhibits are effective. “It is just human nature not to bite the hand that feeds you,” he said.

Mr. Koch, who has given $100 million to Lincoln Center to renovate the former New York State Theater and supports many other institutions, has said that his contributions to the museums come from a deep love of science, and from being “blown away and just fascinated” by the dinosaurs on his first visit to the American Museum of Natural History when he was 14. Mr. Koch and his company did not respond directly to a request for comment about the letter.