The companies said the two sides held a constructive meeting earlier Friday at which both agreed to spend the next two weeks ironing out details on how Emirates will cut capacity to help meet a cap Heathrow has placed on the number of passengers moving through its terminals.

Emirates on Thursday issued a rebuke of Heathrow, saying it wouldn’t comply with an instruction from the airport to restrict the number of departing passengers from the airport to 100,000 until Sept. 11, down from 104,000 that had been scheduled. The cap requires airlines to cut flights or move them to alternate airports. Airlines were also asked to stop selling tickets, a measure Emirates initially refused to meet.

Heathrow outlined the unprecedented cap on Tuesday to try to ease congestion at the airport through the summer, the industry’s busiest travel season. So far, passengers have experienced long waiting times at check-in and security, a scourge of misplaced baggage, repeated delays to flights and last-minute cancellations.

Airlines, airports and ground handlers have been battling to rebuild operations and hire enough staff to meet a faster-than-expected recovery in air travel after the pandemic pushed the industry into a historic downturn over the last two years. Other airports have taken similar measures to cap capacity to limit disruption for passengers, including Amsterdam Schiphol Airport and London Gatwick.

In Europe, disruption has been particularly acute. The continent’s aviation industry recovered later than in the U.S., where domestic travel wasn’t interrupted by the web of travel bans and restrictions that was implemented between European states. That left the industry here facing a steeper ramp up, particularly on short-haul trips.

“Emirates agreed the airline was ready and willing to work with the airport to remediate the situation over the next 2 weeks, to keep demand and capacity in balance and provide passengers with a smooth and reliable journey through Heathrow this summer,” the companies said in a joint statement late Friday.

Emirates had operated all of its flights on Thursday and again on Friday, according to a spokeswoman. The airline has agreed to stop selling further tickets on its flights to the Heathrow until Aug. 11, but will continue to operate its existing flights, the companies said in the statement.

Emirates is owned by the emirate of Dubai, part of the United Arab Emirates. Dubai’s own airport was the world’s busiest, by international passengers, before the Covid-19 pandemic whipsawed the aviation industry.

Write to Benjamin Katz at ben.katz@wsj.com