High-speed trains plan links Capital with Glasgow in 15-minute journey
Councillor Aitken was speaking after a presentation to the city's leading business and political figures by UK Ultraspeed, the firm behind the 1.8 billion project.
It would involve Maglev trains, which can reach speeds of up to 311mph, speeding along a concrete guideway between Scotland's two largest cities.
Chief executive Alan James said today that the infrastructure could be in place within five years if the scheme won government and private backing. It would be funded by a private finance initiative and have stations at Glasgow Queen Street, Edinburgh Airport and Haymarket.
Cllr Aitken said the Edinburgh Labour Party would make a campaign for the Maglev project a "top priority" if re-elected next month.
The trains, which are already in use in Shanghai, seat around 500 people and fares in Scotland are projected to be around 8.95 for a single ticket.
Business leaders said today there were still question marks over the scheme, but Cllr Aitken said it was worth support at the highest level. He said: "This is a project that has real ambition and would deliver a number of benefits for Edinburgh.
"It is much more than a transport link, and is definitely something the city should be making a top priority. I see this as the first leg of a longer-term scheme to create a high speed link to London and beyond.
"We can make this work in Scotland and take it elsewhere. You are combining a labour pool of some three million people, which will make us more competitive on an international level."
Maglev trains float on, and are propelled by, a powerful magnetic field along the guideway. Variable electric current provides propulsion and braking. They are faster than the rival TGV bullet trains but consume more power than normal trains and are unproven over long distances.
The proposed route would take the Maglev alongside the M8 for most of the journey to lessen the impact on the landscape, with the rail corridor coming in from the Gyle to Haymarket the most likely link to the city centre.
Ultraspeed claims that the journey between Glasgow and Edinburgh Airport would take about 12 minutes, with a further journey time of about four minutes into Haymarket.
Mr James said: "This is first-rate transport technology that has been proven to work elsewhere in the world and is ideal for Glasgow and Edinburgh.
"Growing congestion on the M8, limited scope for upgrading the existing railways and the need to compete on an international market are all reasons why it makes sense.
"From an inward investment perspective, a link like this will give you the opportunity to present one city in effect and this gives you the potential for enormous economic benefits."
He added: "If everything fell into place, then there is no reason why a Maglev could not be floating on the tracks for trials before we reach the next Scottish elections."
Ultraspeed's proposal would involve the Scottish Executive paying a PFI consortium an agreed "availability fee" when Maglev is running on time, but with these payments offset by fares revenues.
Graham Bell, spokesman for Edinburgh Chamber of Commerce, said: "We definitely support the need for a high-speed rail link between the two cities and the cost of the different options needs to be investigated as a matter of urgency.
"We do have concerns about the Maglev option. The real prize for train links is connectivity to England and the Continent and the technology has not so far been proven at the lengths that are required for this.
"Also, it is incompatible with the rail system we have at the moment, whereas the TGV ideas being thrown around are not."