The Scottish Parliament voted last week in favour of a ban after Nationalists chose to abstain rather than vote with the Tories in favour of the controversial method of gas extraction.
It is opposed by environmentalists who fear it can contaminate water supplies and cause earthquakes. A Scottish Government report last year concluded it could be done safely, but ministers have called for more research and imposed a temporary moratorium in the meantime.
Grangemouth owner Ineos is keen to frack for gas in large swathes of central Scotland and says it could lead to thousands of jobs and boost the economy.
But Labour MSP Claudia Beamish has now written to economy secretary Keith Brown urging him to respect the will of parliament after the Holyrood vote.
“For Scottish Labour, the science is clear, the last thing our planet needs is another fossil fuel,” Beamish’s letter states.
“Failing to deliver a ban on fracking would ignore the will of the Scottish Parliament and the real concerns of people all across the country.
“You have an opportunity now to reflect the new composition of the parliament and work with the centre-left parties to deliver an outright ban.”
But one Scottish union leader attacked the fracking vote.
Gary Smith, GMB Scotland secretary, said: “It resembled something more like a student pub debate; loudly shouting about what you are against but little substance about what you are for. It sums up the Scottish political discourse these days in a nutshell.”