Schumer, who has been on a media blitz this week, appealed to Trump in a letter Thursday morning to establish a czar with a military background to oversee the production of medical equipment, including ventilators and personal protection equipment, under the Defense Production Act. The U.S. is facing a shortage of such equipment as the pandemic overwhelms hospitals and other medical providers.

"America cannot rely on a patchwork of uncoordinated voluntary efforts to combat the awful magnitude of this pandemic," Schumer wrote. "The existing federal leadership void has left America with an ugly spectacle in which States and cities are literally fending for themselves, often in conflict and competition with each other."

Schumer spoke to Trump twice Thursday afternoon, according to the Democratic leader's office. After hearing his position, Trump informed Schumer that he was in the process of sending a "very nasty letter" but would try to stop the letter from being sent, Schumer's office said. Trump said that he would apologize if he was unable to prevent the letter from going out, Schumer's office said.

In his letter, Trump thanked Schumer sarcastically for his "Democrat public relations letter and incorrect soundbites."

The president argued his administration already has a "senior military officer" in place — Rear Adm. John P. Polowczyk, who is heading the supply chain task force at FEMA. He also accused New York of being "very late" to confronting the virus and suggested the Democratic leader would lose a primary, if challenged by Rep. Alexandria Ocasio-Cortez (D-N.Y.). Schumer is up for re-election in 2022.

Schumer has repeatedly called on the president to use the Defense Production Act to increase the supply of medical equipment. Trump recently invoked the law for its first coronavirus use to get General Motors to make ventilators, but it will still take time to ramp up production. The president has also appointed Peter Navarro, the current White House trade adviser, as national Defense Production Act policy coordinator.

Schumer, however, wrote in his letter that Navarro is "woefully unqualified for this task" and chastised members of the administration for conducting separate "shadow" effort "led by equally inexperienced and unqualified people."

The back-and-forth began Thursday morning.