Hungary and Slovakia, landlocked and dependent on crude from a Russian pipeline, are resisting the oil embargo and holding up the approval of the new package of sanctions.
European diplomats have been locked in difficult negotiations to agree a new package of sanctions against Russia, including a ban on Russian oil imports.
Brussels wants to introduce a sixth raft of sanctions against Moscow to increase the cost of its attack against Ukraine and wean Europe's economy off a dependence on Russian energy supplies.
"It's not easy to establish unity," admitted European Commission President Ursula von der Leyen on Friday.
"The countries that are now hesitating are not yet ready. We are sitting together with these countries in Brussels to work out pragmatic things, such as getting alternative oil to these countries."
"I am confident we will get this package on its way, if it takes a day longer, then it will take a day longer."
But Hungarian Prime Minister Viktor Orban declared the oil ban would cross a "red line" for Budapest.
"The European Commission president, intentionally or unintentionally, has attacked the European unity that had been worked out," he said.
Diplomats in Brussels thought that a compromise could be found, but warned that Orban was using the May 9 Europe Day, celebrating the genesis of the EU, as a lever.
Monday will also be celebrated with great pomp in Russia, when it holds its Victory Day commemorating its World War II triumph over the Nazis.
Brussels hopes to rain on President Vladimir Putin's parade with the new sanctions package.
For the sanctions to go into effect, all 27 EU members must give their unanimous approval.
The plan, drawn up by the commission and submitted to member states on Wednesday as a document that could yet be modified, would halt Russian crude oil imports into the EU within six months and refined oil products by the end of the year.
Hungary and Slovakia, however, would be given an exemption allowing them to keep importing until the end of 2023.
One member state said the discussion was going from talking about delays for some "to a request for exemptions, which pushes the envelope a little too far".
There is also a disagreement over whether to add the head of the Russian Orthodox Church, Patriarch Kirill, a close Putin ally, to the EU's targeted sanctions list. His name was in the commission's draft.
The package also targets Moscow's financial sector, with a plan to kick Russia's largest bank, Sberbank, off the SWIFT messaging system which facilitates transfers between institutions.