In an extraordinary intervention, the airport's chief executive, Gordon Dewar, has voiced concerns in a letter to The Herald that taxpayers' money was being used to distort competition between Edinburgh and Glasgow.
The row broke out after Lufthansa announced on Wednesday it would switch its six-flights-a-week to Dusseldorf route from Edinburgh to Glasgow next April and expand it from a summer-only to an all-year-round service.
Mr Dewar highlighted the role played by Glasgow City Marketing Bureau, which is funded by Glasgow City Council, to lure the airline and claimed Visit-Scotland was also involved.
The Glasgow bureau has confirmed it provided up to £40,000 in marketing support, which it said would help increase passenger volumes.
However, VisitScotland insisted it had not provided any public funds to encourage the move.
Edinburgh Airport was sold by BAA – which still owns Glasgow and Aberdeen airports – to Gatwick owner Global Infrastructure Partners six months ago, following a ruling by the Competition Commission aimed at improving services for air passengers in the central belt.
In his letter to The Herald, Mr Dewar said he supported the principle of competition between Glasgow and Edinburgh, which he claimed had suffered when they were under the joint ownership of BAA.
He added: "I further believe public money and bodies such as VisitScotland can, and should, be used to bring new routes to Scotland, and to ensure their longevity. This is clearly in our national strategic interest.
"On the other hand, I would be extremely concerned if Scottish taxpayers' money was being used to distort competition between two Scottish airports, and if Scotland's public bodies were involved in the commercial negotiations."
A spokesman for Edinburgh Airport said the move by Lufthansa amounted to "cannibalising" routes between the Scottish hubs. He added: "It would be different if public money was being used to support the development of new routes which would benefit the whole of Scotland."
However, the accusations were rejected by Scott Taylor, chief executive of the Glasgow City Marketing Bureau, who insisted Lufthansa's decision to relocate would benefit "the whole of Scotland".
He said: "We have been working with the airline to drive volume into Scotland.
"The marketing support to do this is going to benefit Scotland as a whole, not just Glasgow. Germany is Scotland's biggest source of in-bound passengers and we are helping more Germans reach Scotland."
The bureau has been involved in marketing work in support of developing new air routes since 2007 when the Scottish Government's air route development fund was forced to close due to conflict with European rules on state aid.
Its negotiations with Lufthansa date back to August 2011 and its work has involved several PR agencies in Germany and spending between £20,000 and £40,000 on marketing support.
Mr Taylor said the decision by Lufthansa to relocate was based on feedback on where passengers wanted to fly to, but he added the marketing support would help maximise the number of passengers it carried.
"It's really important we don't take airlines for granted," he said.
"Glasgow needs connections to European hubs and we don't need the permission of another city to compete for them."
Aviation sources believe another factor in Lufthansa's decision to relocate was the presence of Ryanair at Edinburgh, which operates flights to the German cities of Frankfurt, Bremen and Dusseldorf Weeze, located 44 miles from Dusseldorf itself.