Live Nation Entertainment, the biggest power in the concert industry, closed a gap in its ticket refund policy on Friday, after weeks of criticism that the company, and its Ticketmaster subsidiary, were not returning hundreds of millions of dollars that fans had spent on concerts postponed by the pandemic.

“Fans, we hear you,” Michael Rapino, Live Nation’s chief executive, tweeted when announcing the new policy. “We don’t want you to be waiting in limbo while shows are being rescheduled.”

In an earlier announcement, the company set up a 30-day window for requesting refunds when a postponed show was given a new date. But that policy did not apply to thousands of concerts that had been bumped from their original dates but had no new ones — leaving the money fans spent on those shows in a purgatorial state.

According to Ticketmaster — which sells tickets on behalf of Live Nation and many other promoters — about 45 percent of the 30,000 shows so far disrupted by coronavirus fell into this category.

Under Live Nation’s new policy, customers holding tickets to events with no new date will be able to request a refund after waiting 60 days from the time their postponement was announced; they will then have 30 days to ask for their money back. This comes in addition to rules that Live Nation already announced, giving people 30 days to request refunds for shows that have already been rescheduled, starting May 1. Events canceled outright will be refunded automatically.

For example: If a Live Nation concert was postponed on, say, March 15 and had not been rescheduled by May 15, ticket holders would be able to request a refund at that point. They would have 30 days to make the request. (Ticketmaster says it can take a month to process a refund.)

AEG Presents, Live Nation’s biggest competitor, has also announced refunds for rescheduled shows, and a spokesman for the company said it intends to assign new dates to 50 percent of its postponed events by the end of May. But it has not announced a similar plan for giving refunds to events with no new dates planned.

Live Nation and Ticketmaster have been the targets of intense criticism from fans — and from lawmakers — since the early days of the pandemic, who accused the companies of postponing events indefinitely and holding on to money that consumers now need for essentials.

Representative Bill Pascrell Jr., a Democrat from New Jersey, who criticized Live Nation and Ticketmaster’s response, welcomed the change.

“Americans right now don’t know how they’re going to pay for groceries and if they can make rent,” Mr. Pascrell said in a statement. “The last thing they should be worrying about is getting back the money they shelled out for a concert that’s indefinitely on hold.”

One measure of the anger was a class-action lawsuit filed against Live Nation and Ticketmaster this month in California on behalf of a man who says he spent $590 on four tickets to two Rage Against the Machine concerts that were planned for April but have been postponed.

Marie A. McCrary, a lawyer for the plaintiff in that case, said on Saturday that she was unable to immediately review the new policy and declined to comment.

The suit accuses the companies of refusing to provide refunds for rescheduled or postponed events and of deceptive practices, saying that Ticketmaster retroactively revised its refund policy once the pandemic hit. Ticketmaster acknowledged changing the language on its website about refunds but said that its underlying policy has not changed in years.

Sports fans have also pilloried Major League Baseball, which has also been hit by a recent class-action suit. The league sells some tickets through Ticketmaster and has a policy of not offering refunds for postponed games.

That rule is rooted in baseball’s longstanding practice of handling rained-out games, said a league official, who declined to comment on the suit. Rob Manfred, the commissioner of Major League Baseball, said in a recent interview with The Associated Press that the league would “turn over every stone” to salvage the 2020 season.

The rocky rollout of industrywide policies for refunds is to some degree a reflection of the complexity of the music world as it deals with the unprecedented collapse of touring caused by the coronavirus pandemic.

Virtually all events were taken off the road by mid-March, and promoters, talent agents and artists have been scrambling since then to set new dates for shows. Many of those parties have described that process as nearly impossible, since tours are usually set months in advance. Even if a safe date for touring could be determined, tours reaching major venues like stadiums and arenas may have to wait for sports teams — which are often tenants of those buildings — to determine their own schedules before dates can be secured.

“Everyone in the industry is working together to try and save as many of these shows as we can so we can save as many jobs that go with them,” Joe Berchtold, the president of Live Nation, said in a statement. “And we’re trying to reschedule thousands of events at the same time while having very limited information as to exactly when governments will allow venues to reopen. It’s a massive effort and a massive challenge but the entire industry is working through it together.”

Talent agents say that many artists are eager to tour, yet do not want to be perceived as holding their fans’ ticketing money hostage if they wait too long to announce new dates. In recent days a handful of superstar acts, like Bon Jovi, have canceled summer tours outright rather than postpone indefinitely.

“This will enable ticketholders to get refunds to help pay their bills or buy groceries,” Bon Jovi said when announcing their decision.

How many fans will ultimately request refunds is unclear. In a recent note to investors, Morgan Stanley estimated that Live Nation could have to pay as much as $1 billion in ticket refunds this year.

Ticketmaster said that the company has already processed $400 million in refunds, but that for rescheduled events, only 3 percent of customers have requested refunds and that the majority prefer to hold their tickets and attend a new date.

But for fans like Liad Holtzman, a 33-year-old biomedical engineering student, the refund is paramount. In an interview before Live Nation announced its latest policy change, Mr. Holtzman said he had spent about $350 on tickets to two concerts that have been postponed, and has been frustrated in his attempts to get his money back.

“They’re not the bank,” Mr. Holtzman said. “I do not think it’s fair for them to hold my money.”