The EU's executive announced the plans in proposing a joint budget for 2021-27 on Wednesday, a move that could cost Hungary and Poland, two of the biggest net recipients of EU aid, millions of euros.
The funds have been a major driver of investments in Hungary over the past years, contributing to a rise in economic growth to 4 percent in 2017, the highest level in three years.
The Commission did not specify how much of that funding might be in jeopardy. It said any measures taken would be proportionate to the threat a country's actions posed to the rule of law.
"There are treaties in force in the European Union that clearly specify the rights and obligations of EU member states," Foreign Minister Peter Szijjarto told a news conference.
"We do not agree with any proposal that would provide the potential for blackmail of anyone with regard to the payment of EU funds that are due to be given to countries based on the treaties," he said.