Managing director Phil Verster told MSPs they offered a “real practical solution” to easing pressure on the rail network.
Tram-trains, which are being trialled in Yorkshire and widely used in Europe, can run on both tram and train tracks.
They could be introduced in Edinburgh under plans by Network Rail to electrify the “South Sub” to divert more freight trains from running through booming Waverley Station.
The tram-trains could run into the city centre on the line before switching to tracks on streets, which would avoid adding to congestion at Waverley.
Mr Verster was previously involved with the Yorkshire experiment in his last job as Network Rail’s London North East route managing director.
The pilot between Sheffield and Rotherham is due to start running next year.
Mr Verster told the Scottish Parliament’s infrastructure and capital investment committee that tram-trains “must be on the cards for so many cities in the UK.
“They are a real practical solution to get footfall off the rail network.”
The South Sub, which arcs round the southside from near Murrayfield Stadium to Brunstane, lost its regular passenger trains more than 50 years ago but is still used for diverted services and freight trains.
The Capital Rail Action Group, which has campaigned for greater use of the line, said Mr Verster’s support was significant because the ScotRail Alliance covered both train operator and track owner Network Rail.
Chair Lawrence Marshall said: “Tram-trains would ease the pressure on the existing railway and open up new travel opportunities for people moving round the city.”
He said a tram line could be built to link the South Sub to Edinburgh Royal Infirmary, just south of the line.
Stations could be re-opened at Gorgie, Craiglockhart, Morningside, Blackford or Newington, Cameron Toll, Craigmillar, Niddrie and Kinnaird Park.
Infrastructure committee convener and Edinburgh South SNP MSP Jim Eadie led a debate on the issue at Holyrood last month, which secured cross-party support for developing the line.
Transport minister Derek Mackay told the debate: “I am happy to take the issue further, but I give a strong message that I want to see clear evidence from the [public-private co-ordinating body] South East of Scotland Transport Partnership and City of Edinburgh Council that the issue is a priority for them, so that it can be taken seriously, rather than being regarded just as a nice thing to do that is on people’s wish lists.”
Heart of Midlothian, Edinburgh University and Edinburgh Napier University are to be asked to help fund a new feasibility study since stations could serve the Hearts stadium in Gorgie and some of the universities’ campuses.
Tom Hart, of the Scottish Transport Studies Group think tank, said: “I do see future passenger services on the South Suburban, but one of the technical problems is I see Edinburgh tram-trains as being like the Manchester trams with high platforms, with totally segregated access due to freight trains using the route - rather than the ability to walk across tracks at stops.
“This would also have to involve separate high platforms at [on street] tram stops east from Haymarket.”