At another meeting, reserved for medical staff members, some doctors said they were interested in calling a no-confidence vote in the hospital’s top leaders, and asked what steps they needed to take to do that, according to several participants in the meeting.

In an interview Tuesday, Dr. Nadeem R. Abu-Rustum, the president of the medical staff, said a small number of doctors had wanted a no-confidence vote in the hospital’s leadership, but were now satisfied by Dr. Thompson’s decision.

“These same colleagues are not interested in moving forward with a vote of no confidence,” Dr. Abu-Rustum said. “The steps that have been made and taken since the meeting by our leadership have addressed the most important concerns to the medical staff and the associate medical staff and really represents a real progress.”

In addition to resigning his board positions, Dr. Thompson also said Tuesday that Memorial Sloan Kettering would give physicians a greater voice in its operations and would conduct an analysis to understand what had gone wrong at the hospital in recent weeks “so that we ensure our path forward is expertly guided by what we learn.”

Over the past month, articles in The Times and ProPublica have outlined leaders’ ties to for-profit companies, including an exclusive deal the hospital made with an artificial intelligence start-up to license images of 25 million tissue slides. The company was founded by Memorial Sloan Kettering insiders, including a member of the executive board, the chair of the pathology department and the head of a research lab.

After members of the pathology lab objected to the deal, the head of the department announced he would divest his stake.

Another article detailed how a hospital vice president held a nearly $1.4 million stake in a newly public company as compensation for representing Memorial Sloan Kettering on its board. The hospital said last week that a new policy would prohibit compensation in such situations and that the vice president would turn over his stake to the hospital.