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Last week the city council announced top-up payments of £1,000 for drivers in Edinburgh, but Unite the union said national action was still needed.
Mr MacAskill, who is also MP for East Lothian, said: “The taxi and private hire trade has been forgotten and is suffering badly yet are an important part of the economy for the area.
"Its members work hard but along with many others have suffered during lockdown and the level of support has been lower than provided in other parts of the UK. That needs remedied fast.”
The Alba manifesto promises not to leave taxi and private hire drivers behind. As an interim measure, it says it would raise the grant level for taxi and private hire drivers to at least the level in Northern Ireland, to be paid out of the Covid recovery funding provided to the Scottish Government.
And it proposes a capital fund to provide grants and loans for electric and hydrogen vehicle replacement.
Alba candidate Irshad Ahmed said: “The trade needs a boost to recover as lockdown eases but these proposals also offer great opportunities for our communities through an improved environment.
"With COP26 being hosted in Glasgow this should be a chance to transition the trade over from fossil fuels. Grants to allow for electric and hydrogen vehicles to be acquired will make for improved air quality in the city and beyond. Not only does our planet need us to do that but our citizens will benefit from it.”