By Alison Sider and Doug Cameron

Airline executives said people are starting to book flights again, a potential inflection point after the coronavirus pandemic decimated travel demand in recent months.

Top U.S. carriers said Tuesday at an industry conference and in filings that new bookings have started to trickle in and cancellations have slowed.

United Airlines Holdings Inc. said it would restore some capacity in July. Southwest Airlines Co. said its flights are 25% to 30% full. It previously expected its planes to be at most 10% full this month.

"We have seen a little bit of a bounce off the bottom," Paul Jacobson, Delta Air Lines Inc.'s chief financial officer, said at a webcast conference.

Delta said sales have exceeded refunds on some days recently, a reversal of the recent trend. The bookings are a signal of plans for leisure travel in June and July, Mr. Jacobson said.

"But we have to be careful that those actually translate into trips and don't just cancel," he said, adding that even with the uptick, demand is still a fraction of what it typically would be during the usually busy summer months.

Air travel all but ground to a halt in April as lockdowns, international travel restrictions and fear of infection kept people home. Airline executives have said they believe it could take years for demand to return to last year's levels, before the pandemic hit.

The industry is trying to develop common rules to revamp the handling of passengers at airports and onboard aircraft, including temperature checks and the wearing of masks. The International Air Transport Association said Tuesday that it is working with the aviation arm of the United Nations to lobby governments to adopt industrywide standards, which would include screening passengers before they enter airport buildings.

"The restart will go much more smoothly if governments cooperate," said Alexandre de Juniac, IATA's chief executive.

Southwest said new bookings have exceeded cancellations this month so far, and the airline expects its revenue decline in June to be less steep than in previous months, albeit still down 80% to 85% from a year earlier.

Planes are starting to fill up, too, in part because airlines have cut so many flights from schedules. American Airlines Group Inc. said its flights are now 35% full on average, compared with 15% in April. Delta said earlier this week that it would restore 100 flights in June, in part to ensure that planes don't fill up above the 60% cap the airline has set for economy cabins.

United's scheduled capacity for July is expected to be down about 75% from year-earlier levels, compared with May and June schedules that were 90% below the year-earlier levels, the company said.

"We're now seeing a lot of this start to stabilize," said Andrew Nocella, United's chief commercial officer. "Cancellations are coming down, and we start to see North American demand start to inflect and start to look a little bit positive."

Write to Alison Sider at alison.sider@wsj.com and Doug Cameron at doug.cameron@wsj.com