Edinburgh airport said 880,124 passengers travelled through Scotland's busiest hub last month.
Glasgow airport managing director Amanda McMillan said: "It is very encouraging to be able to continue our trend of passenger growth by reporting such positive figures for September. It is also significant that domestic traffic has returned to growth."
More than 100,000 people are expected to pass through Glasgow airport this weekend as part of the October school holiday break.
Edinburgh airport chief executive Gordon Dewar said: "International traffic continues to grow from Edinburgh, perhaps unsurprisingly as we have the most international routes in Scotland. KLM is performing very strongly, which may indicate that an increasing number of travellers are choosing hubs other than Heathrow when travelling internationally.
"Domestic passenger numbers continue to be down versus 2011 but we're confident the forthcoming slot auction will give this market the stimulus it requires."