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"We're starting the negotiation right now but we know very much where it's going", the president said.
Mr Trump noted the two continents together make up more than 50% of the world's trade, and said it would be good if they removed all tariffs and trade barriers as part of the discussions.
Trump agreed on Wednesday to refrain from imposing vehicle tariffs while the two sides launch negotiations to cut other trade barriers.
The leaders also agreed that as long as negotiations were ongoing, "we'll hold off further tariffs and reassess existing tariffs on steel and aluminum", Juncker said.
Jürgen Klopp attacks Sergio Ramos over ‘ruthless and brutal’ final display
Only that now people maybe from [last season], they believe a little bit more, but it doesn't change the situation. "What can I say about that? It's all good.
They also agreed to increase trade in services and agriculture, including greater USA soy bean exports to the EU.
Meanwhile, Mr Juncker also claimed victory, saying a pledge by the USA to hold off on tariffs against cars built in the European Union was a "major concession".
While the US president can claim his aggressive approach is working, consumers, farmers and businesses are feeling the pain from the retaliatory measures imposed to counter the raft of USA tariffs on steel, aluminum and tens of billions of dollars in products from China put in place in recent weeks. "And the media said this would lead to a trade war". Trump said. "Hope they do it, we are ready - but they won't!" he said.
Mr Trump told reporters it was a "very big day for free and fair trade" and vowed to "resolve the steel and aluminium tariff issues".
The US and the European Union have stepped back from a possible trade war, with the announcement of a proposal to ease tensions and avoid more tariffs.
Zimbabwe's Mugabe hopes his former party will lose election
A presidential run-off vote is scheduled for September 8 if no candidate wins at least 50 percent in the first round. Parliamentary and local elections will run alongside votes for the presidency.
These comments contrasted greatly with comments out of Berlin, where the spokesman for Chancelor Angela Merkel welcomed the "constructive" meeting.
The news comes after Trump threatened tariffs on auto imports, and Reuters reported the European Commission is preparing retaliatory tariffs. We will therefore work closely together with like-minded partners to reform the WTO and to address unfair trading practices, including intellectual property theft, forced technology transfer, industrial subsidies, distortions created by state owned enterprises, and overcapacity. "They have gone very dark", Kudlow said, adding that the US remained open to talks if China decides to return to the table.
American stock markets jumped in their last half-hour of trading in response to reports of a US-EU agreement.
Juncker said the United States had agreed to build more LNG export terminals to increase supplies to Europe.
Amazon’s quarterly profit tops $2 billion for first time
Amazon also announced last month that it is buying the online pharmacy PillPack , pushing it deeper into the health care industry. Hiking the annual USA price of Prime 20 percent during the second quarter showed few signs of discouraging sign-ups.