The UK, France, Germany, Spain and other European countries have officially recognized opposition leader Juan Guaidó as interim president of Venezuela.
It comes after President Nicolás Maduro defiantly rejected the EU's Sunday deadline to call snap elections.
Mr Guaidó declared himself interim leader last month and won US backing.
Russia - a backer of Mr Maduro - accused EU countries of meddling in Venezuela's affairs.
As pressure mounted on Mr Maduro to step down, he said he could not rule out the possibility of civil war.
In a TV interview, he warned that US President Donald Trump would leave the White House "stained with blood" if he intervened militarily in the crisis, which has arisen over the legitimacy of his re-election last year.
Mr Guaidó said on Sunday he would build an international coalition to deliver humanitarian aid to Venezuelans.
As head of Venezuela's National Assembly, Mr Guaidó says the constitution allows him to assume power temporarily when the president is deemed illegitimate.
Mr Maduro responded to the EU saying: "We don't accept ultimatums from anyone. It's like if I told the European Union: 'I give you seven days to recognize the Republic of Catalonia, and if you don't, we are going to take measures.'