Party leader Ruth Davidson said it was vital that the SNP did not allow Scotland to get a reputation as a high tax country.
It comes amid reports in today's press that businesses are struggling to persuade highly skilled staff to move to Scotland for fear of higher taxation rates.
She warned that as Labour "eggs on" the SNP to increase taxes, the Scottish Conservatives will demand that the SNP strikes the right balance between fairness and competitiveness.
She also pointed out that many of the proposals in the SNP's plans mirror recommendations by the Independent Commission on Tax led by Sir Iain McMillan in January.
Scottish Conservative leader Ruth Davidson said:
"The hypocrisy of the SNP is incredible.
“After spending years flirting with a local income tax, calling the council tax 'hated' and making endless complaints about it, Nicola Sturgeon has now decided to keep the formula intact, but just put in a few tweaks.
"In fact, the SNP's basic approach today mirrors the proposals put forward by the Conservatives’ independent tax commission published in January.
“It called for a reformed council tax, a more progressive multiplier, protection for low-income households and an end to the freeze but with a cap on any tax rises.
“All of these recommendations have been adopted by the SNP today.
"However, the devil is in the detail and we believe the SNP's changes to the multiplier may be too steep to be truly fair.
“Especially when these changes are added to the steep rises in stamp duty brought in by John Swinney as a cash grab, but which has only resulted in slowing the housing market and creating a black hole in Scotland's finances.
“The SNP needs to be careful that, as a result, Scotland does not get a reputation as a high tax country.
“The result will only be to damage the economy and cut the tax revenues which pay for our school and hospitals.
"While Labour eggs on the SNP to increase taxes ever higher, a strong Scottish Conservative opposition will demand that the SNP strikes the right balance between fairness and the sort of competitiveness that shows people Scotland is open for business.”