The Polish and Hungarian leaders have been joined by Slovenia in rejecting the EU's plan to link funds to respect for the rule of law.
Poland's prime minister hit out at what he called the European oligarchy as the deadlock deepened over linking EU cash with respect for rule of law.
Mateusz Morawiecki said the "oligarchy" punished the weakest states of the bloc and this was not the EU that Poland had originally joined.
His comments came as Poland and Hungary were joined on Wednesday by Slovenia in rejecting the EU's stance, while the European Parliament refused to bend, refusing any concessions.
Poland and Hungary this week vetoed the EU's €750bn coronavirus recovery plan because cash payments to member states would be conditional on their respect for rule of law, which includes democratic values, human rights and the independence of the judiciary.
EU could 'collapse', warns Polish PM
Warsaw and Budapest have frequently been embroiled in clashes with Brussels over such areas in recent years.
"An EU in which there is a European oligarchy that punishes the weakest (of the member states) is not the EU we have entered and it is not the EU that has a future," said Morawiecki.
"We say 'yes' to the European Union, but 'no' to being punished like children. 'No' to mechanisms which mean that Poland and other countries are treated unfairly.
"It is a question of sovereignty," continued Morawiecki, warning that the laying down of conditions such as rule of law could lead to the EU's demise.
“Today you think this instrument is directed against us, against Hungary, maybe against Slovenia, maybe against some other country in central Europe. In a few years, in two or three years, it could be directed against someone else," he added.
"This is a turning point in the history of the EU. Making decisions based on arbitrary provisions in the regulations can lead to its collapse."
EU 'blackmail' over migration — Orbán
Hungary's Prime Minister Viktor Orbán called the EU's proposed rule of law mechanism a "political and ideological weapon" on Wednesday, claiming it was designed to "blackmail" and punish countries that reject immigration.
"In Brussels today, they only view countries which let migrants in as those governed by the rule of law. Those who protect their borders cannot qualify as countries where rule of law prevails," he said in a statement.
Orbán also claimed that rule of law conditions lack objective criteria and don't allow countries sanctioned under the mechanism to seek legal remedies.
“Once this proposal gets adopted, there will be no more obstacles to tying member states’ share of common funds to supporting migration and us(ing) financial means to blackmail countries which oppose migration,” he said.
Orbán and other Hungarian officials have consistently sought to portray attempts in Brussels to rein in Hungary’s democratic backsliding as rooted solely in pressuring the country to accept immigrants.
But EU concerns that Hungary is undermining the rule of law have focused on a wide range of issues, including judicial independence, freedom of expression, corruption, the rights of minorities, and the situation of migrants and refugees in Hungary.
Critics accuse the governing parties in Hungary and Poland of undermining and challenging democratic principles, which both countries deny.
Slovenia’s Prime Minister Janez Jansa, a close ally of Orbán, gave his support to Hungary and Poland.
In a letter to top EU officials Ursula von der Leyen and Charles Michel, Jansa said even though Slovenia supports respecting the rule of law in all cases, "discretionary mechanisms that are not based on independent judgement but on politically motivated criteria cannot be called 'the rule of law'."
'No concessions' from European Parliament
The European Parliament will make "no concessions" on the conditionality of EU funding to respect for the rule of law to Hungary and Poland, which have vetoed the recovery plan, its president David Sassoli announced on Wednesday and the leaders of political groups.
"No further concessions will be made on our side," they said in a statement. "The leaders of the European Parliament deeply regret this blockage and reaffirm that the agreements concluded (both on the multiannual budget and on the rule of law) (...) cannot under any circumstances be reopened".
President of the European People's Party Manfred Weber told Euronews he was hoping German Chancellor Angela Merkel could help break the deadlock, but added the rule of law mechanism remained a "red line".
Under the new mechanism, individual EU countries could lose their veto and have funding cut if a majority of other member states back such a move.
The €750 billion coronavirus recovery fund which Hungary and Poland are blocking is part of a €1.8 trillion sum set for the EU's long term budget from 2021-2027, known as Next Generation EU.
EU leaders will next meet via videolink on Thursday, with pressure on Angela Merkel of Germany which holds the rotating presidency of the EU to find a way out of the impasse.