The resident doctors at the NDMC's 450-bedded Kasturba Hospital and Hindu Rao Hospital have claimed that they have not been paid salary since March.
Many doctors and other staff have tested positive for Covid-19 till date at both hospitals.
Doctors of the NDMC are putting their lives and their family members in danger every day, MCDA president Dr R R Gautam said.
"Being the frontline Covid-19 health care workers, they should be paid their due salaries," he said.
"Our association fully and unconditionally support the reasonable demands of the resident doctors' associations, and have further decided that if the salaries of the three months of all doctors are not paid in a week, then we may also be forced to resign en masse from our government services," the letter said.
In the letter, the MCDA said if not that, "then we may be granted permission to take VRS on a mass level".
The resident doctors of colonial-era Kasturba Hospital on Wednesday had threatened to resign en masse if their demand was not met by the authorities.
The Delhi High Court on Thursday initiated a PIL on the issue.
Jai Prakash, chairman of the standing committee of the North Delhi Municipal Corporation, which runs both hospitals said, "The matter is being resolved".
"Representatives of the RDAs of the two hospitals met me on Thursday. We have assured them that we will try to pay their due salaries, if not at once, for one month right now, and then slowly for subsequent months," he said.
"We have explained to them that the MCD is not getting revenues in this coronavirus
situation, so they must consider our constraint too," Prakash said.