The Army Corps of Engineers might not be the most efficient way to provide support to hospitals strained by the coronavirus pandemic, Defense Secretary Mark T. Esper said Tuesday.

Part of the issue is that the Corps of Engineers is not actively involved in construction but rather in the paperwork involved with construction projects.

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“I’m more than willing to send the Army Corps of Engineers out to work with states to see what we can provide,” Esper said. “The Corps of Engineers is a contracting body that does program oversight work, and if we can be useful, if we can help, I’m certainly willing to provide that service.”

On Sunday, New York Gov. Andrew M. Cuomo called on President Donald Trump to deploy the Army Corps of Engineers to help expand the capacity of hospitals struggling to deal with the COVID-19 outbreak in the state.

At a press conference Tuesday, Trump said he had discussed the idea with Cuomo.

“We have to give them the go-ahead if we find that it’s going to be necessary,” the president said of the Army Corps. “We think we can have quite a few units up very rapidly.”

But Esper cautioned that there were limits to what the Defense Department could actually provide. In terms of ramping up the participation of medical personnel from department to help with the pandemic, that would mean either pulling personnel from military facilities or, for reservists, shifting them from where they are already being used in their civilian capacity.

The Pentagon is providing 5 million N95 respirator masks and 2,000 field-deployable ventilators from its strategic stockpiles to the Department of Health and Human Services, Esper said. The country will likely need more than 2,000 additional respirators, but the hope is they can help give the private sector more time to ramp up production, he said.

There are currently more than 1,560 National Guard members who have been activated by governors in 22 states, according to the National Guard Bureau. More than 650 of those are in New York, where they are assisting with drive-through testing sites and cleaning public spaces in New Rochelle, which has been a particular hotspot.

In addition, they are staffing a New York State call center, said Col. Richard Goldenberg, a New York National Guard spokesman.