But senior administration officials have criticized Mr. Azar for what they believe was a decision to leave key health figures off the task force early on, particularly Dr. Stephen Hahn, the F.D.A. commissioner and an accomplished oncologist, and Seema Verma, the administrator of the Centers for Medicare and Medicaid Services, the agency in charge of health care for tens of millions of older and poor Americans, absences the officials attributed to petty turf wars.
A health and human services official defended Mr. Azar, saying that the department included the Medicare agency and the F.D.A. in coronavirus meetings well before the two joined the task force.
Ms. Verma, who has feuded so intensely with Mr. Azar that it led to an intervention from Mr. Trump, was a top Indiana health official during Mr. Pence’s time as governor in the state, as was Dr. Jerome Adams, the surgeon general, another new member of the task force.
Joe Grogan, the White House Domestic Policy Council director who has feuded with Mr. Azar over drug policy, and Larry Kudlow, the president’s top economic adviser, have irritated some health officials over comments they made about the potential economic impacts of virus containment.
At one point early in the crisis, while the president was at the World Economic Forum in Davos, Switzerland, Mr. Grogan tried to consolidate coronavirus work within the Domestic Policy Council, which the National Security Council had taken the lead on at the White House, irking health officials.
At times the internal tensions have broken out in the open. In an Oval Office meeting last week, Mr. Trump was told that Dr. Redfield had told Politico reporters about a looming shortage in materials the C.D.C. uses to extract genetic material from patient samples.
After Mr. Trump asked about the supply problem, Mr. Azar turned to his C.D.C. chief and asked whether he was going to answer the president, according to three senior administration officials who heard about the testy exchange.