President Donald Trump's administration has been threatening since last year to impose tariffs on auto imports to defend the US automaking sector, a symbol of American manufacturing.
EU governments on Monday backed the move launched by the European Commission two years ago to protect Europe's creative industries, which employ 11.7 million people in the bloc.
A joint statement issued after the talks in Brussels said Juncker had again warned that November's withdrawal agreement could not be renegotiated -- after May came hoping to persuade Brussels to change the so-called "backstop" clause for the Irish border.
"We agreed with Trump on a kind of ceasefire when it comes to new car tariffs," Juncker told German broadcaster ZDF.
Trump rejected an EU offer to eliminate tariffs on cars and said the EU's trade policies are "almost as bad as China.
The leaders of the 27 countries remaining in the European Union will give the go-ahead on Friday for the EU's chief negotiator Michel Barnier to begin talks with London on a transition period and future trade ties with Britain.
EU Commission spokeswoman Mina Andreeva said on Twitter that they were "likely to meet this morning at 7:00 AM (0600 GMT) in the Berlaymont", the organisation's headquarters.
May would probably meet the European Commission president at 7 a.m. (0600), the Commission said in a statement, with a news conference to follow half an hour to an hour later. It gave no other details.
An early morning meeting in Brussels between Juncker and British Prime Minister Theresa May, whose efforts to reach a deal broke down in failure earlier this week, was also a possibility, Juncker's spokesman said.
May's office said the meeting was long planned but gave no details. The dinner was not on Juncker's agenda published on Friday, however, and EU officials said it had also not been on the schedule for Brexit negotiator Michel Barnier, who will be at the dinner along with his British counterpart, David Davis.
Noting that the Brexit talks expected to be launched next month would last two years before Britain withdraws from the bloc, Juncker said in a speech to the Belgian parliament: "To agree on the future architecture of relations between the United Kingdom and the European Union, we will need years."
"The president is not going to resign," a Commission spokesman told a news briefing when questioned about the report in Der Spiegel that Juncker had threatened to quit if European Parliament President Martin Schulz has to give up his post.
The European Union held a summit to sign a trade deal with Canada that was seven years in the making and had exposed some of the difficulties of sealing a trade pact. The Canadian deal was held up for weeks, most notably due to obstruction from regional governments in Belgium.
The ceremony had been pushed back from Thursday after French-speaking Wallonia, with just 3.6 million people, initially vetoed a deal affecting more than 500 million Europeans and 35 million Canadians.
British Prime Minister Theresa May on Friday called for "give and take" in negotiations with the European Union (EU) on the UK's exit from the 28-nation economic bloc.
Meeting in the Slovak capital with the British conspicuously absent, the 27 other EU members unveiled a six-month "road map" of measures designed to restore public confidence in Europe's ailing common project.
In setting out the Commission's plans for the first time since the UK voted to exit the EU on June 23, Juncker highlighted the British referendum as a warning that the EU faces a battle for survival against nationalism in Europe.
Former Polish premier Tusk added that the bloc must be less "politically correct" and protect Europeans worried about terrorism, security and globalisation in the wake of Britain's vote to leave.
Juncker also said that he expected Britain to trigger Article 50 very soon after Cameron's successor is named on September 9.
Senior diplomats from founding powers Germany and France, as well as several other countries, met on Monday for talks chaired by European Commission President Jean-Claude Juncker's chief of staff, Martin Selmayr, several sources said.
EU state aid regulators aim to rule on Amazon's tax deal with Luxembourg by July, two people familiar with the matter said on Thursday, and it may order the country's tax authorities to recover about 400 million euros (USD448 million) in back taxes
An agreement on the first tranche of the credit was signed in Brussels on Wednesday during the 13th EU-India summit attended by Prime Minister Narendra Modi.
The European Union's two top figures, Donald Tusk and Jean-Claude Juncker, presented its 28 leaders with draft proposals at a long-delayed dinner after hours of painstaking face-to-face talks on an issue that threatened Britain's place in the union.
European Commission President Jean-Claude Juncker drew a direct link between the two key achievements of EU integration, telling the European Parliament the euro would be jeopardised if the Schengen passport-free travel system unravels.
The ministers were holding emergency talks to discuss plans unveiled last week by European Commission chief Jean-Claude Juncker to redistribute 120,000 refugees from overstretched Greece, Italy and Hungary.