After Sunday's deadline passed, a flurry of statements was issued by France, the UK, Germany and Spain and the other countries that now recognise Mr Guaidó as interim president.
Many of them pressed Mr Maduro to call new elections.
French President Emmanuel Macron said Venezuelans had the right to "express themselves freely and democratically", announcing his support for an EU contact group.
Spain's Prime Minister Pedro Sánchez said Venezuela "should be the author of its own destiny".
UK Prime Minister Theresa May's official spokesman said that "further steps" were being considered, including the use of sanctions, without outlining what form any possible sanctions might take.
While a majority of EU members back Mr Guaidó, others such as Greece and Ireland called for fresh elections but stopped short of recognising him.
Russia has attacked Monday's statements, accusing EU countries of interfering in Venezuela's affairs and attempting to "legitimise usurped power".
The Venezuelan government said it would "fully review" its relations with the European governments who had recognised Mr Guaidó.
A foreign ministry statement said those governments were "officially submitting to the United States administration's strategy to overthrow the legitimate government of President Nicolas Maduro".
In an interview with Spanish television programme Salvados broadcast on Sunday, Mr Maduro was asked if the crisis in Venezuela could result in civil war.
"Everything depends on the level of madness and aggressiveness of the northern empire [the US] and its Western allies," he said.
President Trump has told US broadcaster CBS that the use of military force is still "an option".
Mr Maduro says he will start collecting signatures from Venezuelans for an open letter to Mr Trump rejecting foreign military intervention.
Source: BBC