Less than a week after twice enticing federal workers to resign, government officials may be walking back their overtures to some aviation safety workers.

During an interview with CNN on Sunday, the new secretary of transportation, Sean Duffy, said that within his agency, which oversees the Federal Aviation Administration, “the critical positions in regard to safety are not offered that early retirement.” He also said that air traffic controllers, among others, were “exempted” from a recently imposed hiring freeze.

“We’re going to keep all our safety positions in place,” he said. “No early retirement.”

One of the resignation offers, which would allow workers to be placed on paid administrative leave until the end of September, arrived just 24 hours after a passenger jet and an Army helicopter collided on Wednesday, killing 67 people near Washington’s Ronald Reagan National Airport. The offers, which the Office of Personnel Management made via email on Jan. 28 and Jan. 30, rattled F.A.A. workers, many of whom were still reeling from the worst aviation accident in recent U.S. history.

Staffing in the critical area of air traffic control has been chronically low for years and may have played a role in the collision. Yet some air traffic controllers, who believe they have long been overworked, are considering resigning, according to two controllers who requested anonymity because they were not authorized to speak publicly.

The F.A.A. and the Department of Transportation did not respond to questions on Monday as to how they would reverse the resignation offers, which were issued to a broad spectrum of federal workers.

But a notice from the National Air Traffic Controllers Association, the union that represents controllers, appeared to back up Mr. Duffy’s assertions.

The notice, which was distributed on Sunday and seen by The New York Times, pointed to guidance issued Jan. 28 — part of which was directed to agency heads and part of which provided more detailed directions to agency human-resources managers — stating that agencies had the right to exempt certain workers from what it called the “deferred resignation” program.

Deferred resignations, stated the memo, would be unavailable to military personnel, postal workers, and employees working in immigration enforcement and national security, as well as “any other positions specifically excluded by your employing agency.”

Mr. Duffy said on CNN that “all our safety positions” — which he had said a moment earlier included air traffic controllers and inspectors — would be exempted from “early retirement.”

In its notice to members, NATCA recommended workers “do not submit a deferred resignation letter until we receive additional information on how it would affect your retirement, benefits, and what positions are excluded.” The union added that it had asked for an F.A.A. briefing on those questions.

A spokesman for NATCA confirmed the email but declined to elaborate on whether the union had learned additional details about the resignation push.