Tui, the UK's biggest travel firm, has suspended its beach holidays for the next five weeks.
The company has cancelled all trips up to and including May 14, while its Marella Cruises sailings have been axed until at least June.
A spokeswoman said: "We are constantly monitoring the situation and will start taking people on holiday again as soon as we are able to do so.
"At this point in time, nobody can accurately predict when that will be, so for the time being we will keep a close eye on our programme and continue to amend and adapt timings in line with the latest global travel advice."
She added that customers with a cancelled booking "will be able to amend their holiday to any other Tui package holiday on sale" via its website.
The firm did not say that consumers would be entitled to a refund.
Under EU law, travel companies must offer to refund customers within 14 days if their package holiday is cancelled.
But the industry has warned that many firms will be unable to survive if they are forced to pay out immediately.
Trade association Abta has called for the UK Government to follow measures taken in other European countries to allow holiday companies to issue credit notes instead of cash refunds due to the deluge of claims caused by the coronavirus pandemic.
Elsewhere, Jet2 holidays and Jet2.com say their flights and holidays will resume in June.
The operator released a statement on Tuesday (April 7) to say they had taken the decision to recommence operations on June 17, 2020.
However all bookings scheduled to depart before this date would now be cancelled due to the ongoing coronavirus pandemic.
In a post shared on their official social media channels, a spokesperson said: "In view of the ongoing uncertainty caused by the COVID-19 pandemic, we have taken the decision to recommence our flights and holidays programme on June 17th.
"This means for customers travelling before this date, unfortunately your flights and holidays will not be operating.
"We will be contacting all affected customers to discuss their options, one of which is rebooking to a later date. We are contacting all customers in departure date order which we believe is the fairest way to handle this.
"The number of calls we have been receiving is unprecedented so you do not need to make contact with us. Please do bear with us, and we thank customers in advance for their loyalty, understanding and patience."
