It comes after the airline initially refused the airport’s demands to cut capacity, describing the request as "unreasonable and unacceptable".
However, following a meeting between Emirates president Sir Tim Clark and Heathrow chief executive John Holland-Kaye, the two came to an agreement to help the airport "remediate the situation".
In a joint statement issued by Clark and Holland-Kaye, they said: "Emirates agreed the airline was ready and willing to work with the airport to remediate the situation over the next two weeks, to keep demand and capacity in balance and provide passengers with a smooth and reliable journey through Heathrow this summer.
"Emirates has capped further sales on its flights out of Heathrow until mid-August to assist Heathrow in its resource ramp-up, and is working to adjust capacity. In the meantime, Emirates flights from Heathrow operate as scheduled and ticketed passengers may travel as booked."
