Austria's chancellor Christian Kern criticised Mr Trump's travel ban on seven majority-Muslim countries and suggested that the United States shared responsibility for the refugee crisis because of its military interventions.
Speaking to reporters as he left the summit, Hollande said the USA should pick an envoy who believes in Europe.
As if to underline the distance from the White House at which the European Union now finds itself, it was left to Theresa May, leader of the country that's exiting the alliance, to brief her counterparts.
Arriving at the 16th century Grandmaster's Palace in Valletta on Friday morning, French president Francois Hollande said there was no future in relations with Mr Trump unless those relations were "defined in common".
"It can not be accepted that there is, through a certain number of statements by the president of the United States, pressure on what Europe ought to be or what it should not be", he said.
Ms Merkel said she was "gratified" that the Prime Minister had said she wanted to see a "strong EU", even after Britain had left.
Ms Wallstrom told BBC radio: "No I don't think that that is in the making at the moment".
"This is the European way, the American way might become different today, this is not a European problem, this might be an American problem", she said, adding that the EU will seek cooperation and friendship as always with the U.S. Trump has since reaffirmed America's commitment to it. But she added that there was also a "clear recognition" that Europe needs to step up its independent defense capability.
European countries sometimes complained that President Obama neglected them in favor of a focus on Asia.
In Asia, Mattis vows joint stance against N. Korean nuclear threat
He also jolted the region by pulling Washington out of an Asia-Pacific trade deal that Japan had championed. Washington and Seoul maintain THAAD is strictly to protect against North Korea.
European leaders called for a unified response to Donald Trump's policies following the summit in Malta.
Dalia Grybauskaitė, the Lithuanian president, was dismissive of Mrs May's efforts to forge a friendship with her visit to the White House last week.
Kern said: "It's not acceptable for the global community if America shirks responsibility".
Some EU leaders heavily criticised Donald Trump's decision to ban refugees and people arriving to the U.S. from seven Muslim-majority countries.
"We must not imagine some sort of external protection", he said.
"Who knows what the president of the United States really wants (on NATO)?"
"We have to be tough", said Trump, who entered office with an approval rating of about 50 percent. What matters is solidarity at the European Union level.
On Friday, the Portuguese parliament voted to condemn Trump's U.S.travel ban on immigrants from seven predominantly Muslim countries and highlighted the United States' important role in promoting tolerance and human rights around the world.
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