"The entry bans against seven Muslim countries are... highly problematic," Kern said before an EU summit in Malta. "We should win them over in the fight against Islamism and not define them as adversaries.
"There is no doubt that America shares responsibility for the refugee flows by the way it intervened militarily ... It is unacceptable for the international community that America wants to evade its responsibility on this," he added.
EU leaders at the summit in Malta are set to discuss relations with Trump, after major talks about cutting illegal migration across the Mediterranean from Libya.
Kern has said that it's Europe's responsibility to control migration and not leave asylum seekers at the mercy of people smugglers. He added that Europe also has a duty to look beyond its own borders and monitor the conditions in refugee camps.
He told reporters that he was keen to discuss the ‘Brexit' process with British Prime Minister Theresa May before the summit begins, as Austria will assume the EU Presidency in 2018.
Meanwhile, the French President Francois Hollande has criticised "unacceptable" pressure on the European Union from Trump, who has predicted a break-up of the bloc. "It is unacceptable that there should be, through a certain number of statements by the president of the United States, pressure on what Europe should or should not be," Hollande told reporters.
"Who really knows what the US president wants, particularly for the transatlantic alliance, and on the sharing of expenses that he calls a burden," Hollande added.
Asked what he thought about the apparent support for Trump coming from the leaders of Poland and Hungary, Hollande said "There can be no future with Trump if it is not defined together" by the EU, adding that "what is at stake is the destiny of the EU".
"A lot of countries should think that their future is first with the EU, rather than imagining who-knows-what bilateral relationship with the US."
Trump has alarmed many in Europe by backing Britain's decision to leave the EU, predicting that more countries will jump ship and calling the US-led NATO military alliance "obsolete".
German Chancellor Angela Merkel meanwhile said the best way for the 28-nation bloc to deal with a US administration that seems ambivalent to Europe is to push forward with its own plans.
"I already said that Europe has its destiny in its own hands," Merkel told reporters as she arrived in Valletta.
"And I believe the stronger we state clearly how we define our role in the world, the better we can take care with our transatlantic relations," she added.
"That is why for me, talks about Europe are here in the foreground and not to deal with other parts of the world."