Plans to replace air passenger duty with a discounted Scottish alternative have been delayed until at least 2020.
Scottish ministers want to set up a devolved air departure tax (ADT), and would immediately cut the levy by 50%.
However, the plans are tied up in legal issues, and ministers now say they will not be resolved until after April 2020.
A group of air industry bosses urged ministers to "get on with it sooner rather than later, or be up front with us that it's never going to happen".
And opposition parties at Holyrood called on the government to scrap the tax cut plans altogether.
The Scottish Parliament was given powers to charge tax on passengers leaving Scottish airports under the Scotland Act, which came into force in 2017, and MSPs passed a bill to set up a devolved tax later that year.
The SNP has a longstanding policy to cut the new tax by 50%, before eventually scrapping it entirely - a move it says will boost the economy by increasing the number of flights in and out of the country.
However, the plans ran into problems with EU state aid rules, which currently see airports in the Highlands and Islands given an exemption.
Scottish and UK government officials have been working together to solve the issue, but Scottish Economy Minister Kate Forbes told MSPs that "a solution has not been found that would be ready for introduction at the beginning of the next financial year".
She said that this "taken together with the continued uncertainty around Brexit" meant that the introduction of the new tax would have to be deferred "beyond April 2020".
She added: "We are doing all we can to work with airlines and airports to help grow the direct routes which are important for our tourism sector and Scottish businesses."
However, a joint statement from groups including Airlines UK and the owners of Aberdeen, Glasgow and Edinburgh airports said the government "needs to be straight with industry".
They said: "This was a cast-iron manifesto commitment and they have now failed to implement it two years in a row, and in the meantime it is Scottish tourism and connectivity that is suffering.
"The message from airlines and airports is clear - either do what you have promised and get on with it sooner rather than later or be upfront with us that it is never going to happen."
Labour, the Greens and the Lib Dems all called on the government to scrap the planned tax cut, saying it was undeliverable and would harm efforts to tackle climate change.
The Scottish Conservatives back cuts to some airline taxes, but said the SNP's handling of the matter was a "complete shambles".