United Airlines on Friday warned that it expects a lengthy slump in travel demand because of the coronavirus, which will likely require the carrier to have a smaller workforce, while Delta asked for more volunteers to take unpaid leave after close to a quarter of the carrier's employees raised their hands.

The comments came after President Donald Trump signed a $2 trillion government coronavirus relief package that included billions in grants for airlines to keep paying workers through the end of September.

"Based on how doctors expect the virus to spread and how economists expect the global economy to react, we expect demand to remain suppressed for months after that, possibly into next year," CEO Oscar Munoz and United's president, Scott Kirby, who's scheduled to take the helm in May, wrote in a message to employees. "That means being honest, fair and upfront with you: if the recovery is as slow as we fear, it means our airline and our workforce will have to be smaller than it is today."

The message was the latest in a series from executives who do not expect a quick U.S., or global, recovery from the coronavirus pandemic. The United States has detected more than 97,000 cases of COVID-19.

Layoffs or furloughs at United, which had about 96,000 employees as of the end of last year, aren't imminent. The coronavirus aid bill provides $25 billion in grants to U.S. passenger airlines, granted they do not furlough or cut the pay of their workers through Sept. 30. United executives committed to that on Friday.

United is seeking to cut its costs by asking employees to take unpaid leave, while some staff is working a reduced schedule. Airlines including United, are seeking to exhaust voluntary leaves, including early retirement plans, before turning to furloughs or layoffs.

Delta Air Lines CEO Ed Bastian on Friday also said the company wouldn't cut pay or furlough workers through that period and said the government aid wouldn't solve the slump in demand.

"While this assistance is welcome, it's important to remember that the relief package is not a cure for the unprecedented challenges we face," Bastian told employees in a memo. Some 21,000 workers have volunteered for unpaid leave of various periods.

The toll from the virus and draconian measures such as stay-at-home orders to stop it from spreading are already reverberating throughout the U.S. economy. Unemployment claims surged to a record 3.28 million in the week ended March 21.

U.S. airlines, which employ some 750,000 people, have been among the businesses hardest hit by the coronavirus. Strict travel restrictions and concerns about contracting the disease while traveling have driven down demand. A fragile economy will also mean fewer lucrative business trips and vacations for consumers.

Airlines have slashed flights, parked hundreds of jets and asked thousands of employees to take unpaid leave, while they tap credit lines to shore up cash. Their international operations have been cut to the smallest in decades.

Executives have warned that even their reduced schedules are drawing few travelers. Chicago-based United has cut its April schedule by more than 60% and expects planes to fly less than 20% full or in the single digits in some cases, the executives said.

The company plans to hold a "virtual town hall" meeting with employees on April 2.

Kirby and Munoz praised their employees and a "deep-seated culture of caring for one another."

"So when travel demand returns — and it will return — we will bounce back and be ready to accelerate towards our goal of becoming the best airline in the history of aviation," they said.