An assessment of how much each Scottish firm will pay in non-domestic rates is under way, to take effect from April.
Tory leader Ruth Davidson has written to Nicola Sturgeon calling for an "urgent review" of the process.
The first minister has said all businesses will have the chance to appeal the final valuations.
And she said that 100,000 small firms would be lifted out of having to pay rates altogether via the small business bonus scheme, claiming Scotland has "the most competitive business rates regime in the whole UK".
The revaluation of how much firms have to pay is being carried out by independent assessors, funded by local councils. The Scottish Assessors Association has published provisional values, with the finalised figures to be sent out in March before they take effect in the new financial year.
The last revaluation in Scotland was carried out in 2010.
The Conservatives said they had been "inundated with letters from businesses across Scotland who are facing huge increases in their rates", claiming some faced having to pay four times more than they did previously.
The Scottish Tourism Alliance has also requested a meeting with Ms Sturgeon to discuss what they called "crippling" rates increases, while the Scottish Chambers of Commerce have also raised concerns.
Ms Davidson said: "These shops, hotels and restaurants are vital to our economy, providing much needed jobs in many areas of the country, and we cannot afford to see them simply go out of business.
"That's why I've called on Nicola Sturgeon to listen to the voices of these businesses and the Scottish Tourism Alliance and launch an urgent review into these rate increases.
"The amounts that are being asked for are clearly unsustainable and if immediate action is not taken then we risk seeing a huge amount of damage done to our economy."
A review group led by former RBS chairman Ken Barclay has been set up to "enhance and reform" the business rates system in Scotland, although it will not report back until after the new rates have come into force.
Ms Davidson and Ms Sturgeon have clashed over the matter in the Holyrood chamber in recent weeks, with the first minister noting that "competitive business taxes are important".
She said: "The final valuations will be issued later this year and all businesses will have the opportunity to appeal if they think that their valuation is wrong.
"We have the most competitive business rates regime in the whole UK, with 100,000 small businesses having been lifted out of business rates altogether.
"We have a tourism sector that, thanks to the good work of those in it, is booming, and the employment level is rising much faster than it is in the rest of the UK. We are also the best-performing part of the UK outside south-east England for inward investment.
"Those are the success stories of the Scottish economy, and we will continue to invest in the success of our economy. We will also protect our public services and those on low incomes."

Rowan County Clerk Kim Davis stopped issuing all marriage licences the day after the US Supreme Court legalised same-sex marriage.
The American Civil Liberties Union has sued her on behalf of four couples, two gay and two straight.
In court on Monday in Covington, Kentucky, Ms Davis said issuing the licences would violate her religion.
"If... I authorise that I'm saying I agree with it, and I can't," she said.
The state's governor, Steve Beshear, said county clerks must issue marriage licences to same-sex couples immediately after the Supreme Court's ruling.
Two clerks in the state refused. They can only be removed from office by the state legislature.
US District Judge David Bunning will not rule on Ms Davis' case until August, he said.
Mr Bunning could order Ms Davis to issue licenses, impose a fine or put her in jail.
Ms Davis wants Mr Beshear to pass a law protecting county clerks and allow people to get marriage licences online.
The governor refused to call the legislature back into session to do so.
The Scottish Conservatives have called for an "immediate review" of the business rates revaluation after firms raised concerns about tax increases.
[NEXT_CONCEPT]
A Christian official has defended her refusal to issue marriage licences to same-sex couples in Kentucky.