Some 7.3 million passengers travelled through Heathrow last month, up 0.1% on August 2015.
Growth at the west London hub was driven by a 9.7% rise in travellers heading to or from the Middle East, while the Latin America market was up 5.8%.
Passenger numbers in the UK sector were down 10.7%, while Africa flights saw a fall in passengers of 4.8%.
The airport also welcomed Great Britain's Olympic team on their return from Rio last month.
Heathrow chief executive John Holland-Kaye reiterated his call for the building of a third runway to be given the go-ahead by the government.
He said: "We were delighted to welcome the golden heroes of Team GB back from Rio. They have shown that Britain can be successful against tough international competition by backing our winners.
"Britain should not accept bronze, when we could so easily win gold. So now is the time to back the winners in our economy and expand Britain's biggest and most successful port, Heathrow.
"We can get exporters, large and small, from all across Britain connected to the growing markets of the world, and it is urgent that we get on with it.
"That is why we are looking at options to connect Britain to growth quicker and cheaper."
Gatwick also recorded its busiest ever August, with 4.8 million passengers travelling through the airport, a 5.7% increase on last year.
A 51% boost in passengers using North Atlantic routes fuelled the growth. The Ireland market was up 12.8%, while the UK sector increased by 9.1%.
Gatwick chief executive Stewart Wingate claimed the figures demonstrate errors made by the Davies Commission, which recommended in July 2015 that Heathrow should be expanded rather than Gatwick.
He said: "Gatwick is delivering for Britain today and, with a second runway, will continue to deliver the crucial growth we need now more than ever.
"The Airports Commission said that Gatwick could not deliver long-haul routes, yet we have added 20 this year alone, putting us in the premier league of airports in Europe that serve 50 or more long-haul links.
"The Airports Commission also said that we would not serve 42 million annual passengers until 2030, yet we passed this mark just days ago.
"Our growth and success illustrates that Britain needs to put the failed plans of the past behind it and back the plan that can actually deliver, and deliver cheaper, faster, simpler and with absolutely no taxpayer subsidy. It's time for growth and certainty, it's time for Gatwick."
Some 2.9 million passengers travelled through Manchester Airport last month, up 9.1% on last year.
The airport's chief executive, Ken O'Toole, said: "August is always the busiest month of the year for the airport as families get away during the school holidays and it was no different this year.
"Spain has certainly proved popular, which reflected the increase in capacity we saw from airlines to the likes of the Balearics and the Costas.
"New long-haul services that have launched this summer to destinations like Boston, Los Angeles and Beijing have all contributed to a record summer for Manchester Airport.
"With new routes being recently announced to Houston, Tobago, Phuket and Mauritius, passengers will soon benefit from an even greater range of long-haul destinations directly from Manchester."
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