But the socialist leader showed no signs of caving in and lashed out at the European Union and the Trump administration, which has also put pressure on the Venezuelan government by imposing sanctions on Venezuelan oil exports and demanding Maduro's departure.
Seven EU states had given Maduro a Sunday deadline to call presidential elections or they would recognize Guaido.
"The people of Venezuela have suffered enough". They meet after European nations this morning made a coordinated announcement to recognise rival Juan Guaido as leader.
Austria, Sweden and Denmark also recognised Guaido.
Mr Guaido, who leads the National Assembly, declared himself caretaker leader last month in a move splitting worldwide powers and bringing Venezuelans onto the streets. "Venezuela won't be governed from Madrid", he added.
"The most important issue now is to get Europe in line and to deepen the isolation of Venezuela and its backers", said a government official in Bogota, who spoke on condition of anonymity.
But he stopped short of breaking off diplomatic relations with the 16 European countries that recognized his rival Monday, unlike his swift move to cut off ties with the USA after it threw its support behind Guaido last month.
Tens of thousands of Venezuelans have turned out in recent protests to demand Maduro's exit, although he appears to have the support of the nation's powerful military and security services.
"In Venezuela, there will be peace, and we will guarantee this peace with the civil military union", he told state television, in the company of khaki and black-clad soldiers who were earlier shown carrying guns and jumping from helicopters into the sea.
Mr. Trudeau also took the opportunity to recognize Mr. Guaido's representative to Canada, Orlando Viera-Blanco.
Speaking to reporters in Brussels after a meeting of European Union foreign affairs ministers, top EU diplomat Federica Mogherini said that "the EU and its member states never recognised as legitimate the presidential elections that were held a year ago [in Venezuela]".
"Any solution to the internal political crisis in Venezuela is possible only by Venezuelans themselves", the Kremlin spokesman stressed.
"I don't accept ultimatums from anybody", Maduro told Spanish TV channel La Sexta in an interview broadcast late Sunday.
"They are trying to corner us with ultimatums to force us into an extreme situation of confrontation", Maduro said.
Mr Maduro has ignored this call.
Guaido is expected to announce a date for the arrival of humanitarian aid from the USA - a path Maduro believes will lead to a US-led military intervention.
"They use sledgehammers instead of boxing gloves", President Maduro said, accusing the United States of seeking his removal so that it could take control of Venezuela's vast oil reserves.
Jon Snow is joined by the Labour MP Chris Williamson, who like Jeremy Corbyn, has supported the Chavez and Maduro governments in Venezuela.
It is time for a new start, with free and fair elections in accordance with worldwide democratic standards.
The moves by European powers further isolate Maduro, who has already lost the recognition of a host of nations, including the United States, Canada, Brazil, Colombia, Argentina and Israel.
The 35-year-old Guaido, accused by Maduro's government of staging a US -directed coup, has galvanized Venezuela's opposition with a hopeful message.