Mr Salmond said the tax on air fares – which passengers pay when booking flights and which is charged at different rates – was damaging Scotland, business and tourism and was an unfair extra cost for passengers.
He said he would also raise the issue of British Airways being the only carrier between Glasgow and Heathrow, leading to higher fares.
Mr Salmond said it would be on the agenda when he and others met Mr Cameron at the Joint Ministerial Committee.
He said: "There is an overwhelming urgency in this matter. I know other devolved administrations share my view that Air Passenger Duty would be an important weapon in terms of attracting more direct flights to and from Scotland.
"Even if there was an extra runway at Heathrow it would not solve the difficulty we have. When Heathrow is clogged up it is not just the case that people have difficulty getting to Scotland, but they are deterred from coming as a result of the extraordinary congestion.
"We need more direct flights and one way of getting more direct flights is to use Air Passenger Duty as an important means of doing so."
Politicians, airport bosses and business leaders in Glasgow have been calling for Air Passenger Duty to be devolved or reduced to attract new routes to the city for many years.
The city council and Glasgow Chamber Of Commerce say more direct flights to European and American routes are needed to remove the necessity to travel through Heathrow or other London airports.
If passengers fly into London and then on to Glasgow they incur the taxes of an extra flight, as well as the extra air fare, which is seen as a disincentive for some people to come to Glasgow.
An economy flight between Glasgow and London will incur APD of £13, any connecting flight further afield would be subject to further tax of as much as £92 for long haul. Business class flight taxes are double.
Mr Salmond also said concerns about limited flights between Glasgow and London would be raised with the PM.
He said: "BA is the only operator in the Glasgow- Heathrow route since April 2011 when BMI withdrew.
"We will be raising concerns about the lack of competition on the route and the mounting evidence that that has been detrimental to passengers both in terms available space, landing slots and on the prices people are being asked to pay."
stewart.paterson@ eveningtimes.co.uk
