Economy Minister Mihaly Varga said Tuesday that the tax -- 150 forints (0.50 euros, $0.61) on each transferred gigabyte of data -- was needed to plug holes in the 2015 budget of one of the EU's most indebted nations.
The idea has triggered alarm, including from Nellie Kroes, the EU's digital chief, who tweeted that the tax was "a shame for users and a shame for the Hungarian government".
Governing right-wing party Fidesz, led by Prime Minister Viktor Orban, later proposed capping monthly payment at 700 forints (2.3 euros, $3) for consumers and 5,000 forints for , but the move has failed to calm anger.
Some 36,000 people have signed up to a protest organised on social media to be held outside the Economy Ministry Sunday to demand the tax be scrapped.
Organisers told AFP Saturday via email that the tax would restrict access to information, particularly in poor areas, could cripple small , and would restrict government critics who mainly use online media.
The top US diplomat in Budapest warned Friday of "negative trends" such as weakening of the rule of law and intimidation of civil society have "rapidly taken hold" in Hungary, days after Washington issued entry bans on six government officials it suspects of corruption.