As Brussels residents take to the streets in solidarity with American protesters, European leaders are scrambling to comprehend and respond to US President Donald Trump's executive order banning entry to the US for people from seven Muslim countries.

Members of the European Parliament joined hundreds of people who returned Monday to the site of the Brussels attacks memorial to express their indignation and opposition to blocked US entry for citizens of Iraq, Iran, Yemen, Libya, Somalia, Sudan and Syria. The "Refugees Welcome" signs that emerged in the backlash of the March 22 suicide bombings were back, as were new anti-Trump slogans.

"He's not our president but he's our problem," read one sign in French, while another declared "Trump is afraid - Merkel is right." "Neither IS [Islamic State] nor Trump can divide us," proclaimed another.

German Foreign Minister Sigmar Gabriel and his Dutch counterpart Bert Koenders were among the first politicians to issue a formal position regarding the order.  In a statement, the ministers took issue with two aspects in particular, noting that admitting refugees was an "international legal obligation not to be questioned" and that, if counter-terrorism was the goal, "[w]e believe absolutely that entry bans against millions of people on the grounds of their nationality, origin or religion cannot be the right tool."

Amid confusion over what will happen to potential travelers who also hold passports from EU countries, Gabriel and Koenders promised they were "determined to protect the rights of our citizens and will consult within the European Union about the necessary steps."

EU consensus not immediate

EU institutions were also trying to handle the fallout and figure out what's next.

At the European Commission's daily briefing, spokesman Margaritis Schinas stalled any immediate reaction to the policies, saying: "We are taking some time to see how they can have an impact on any EU nations, which is not yet clear."  But Schinas laid out the EU baseline, which puts it in direct conflict with the US order as far as refugees are concerned:  "This is the European Union, and in the European Union we do not discriminate on the basis of nationality, race or religion, not only when it comes to asylum or in any of our other policies."

Schinas was backed by EC Vice President Federica Mogherini. "This is not the European way, for sure," she said after meeting Norwegian Foreign Affairs Minister Borge Brende. "The European Union will continue first of all to take care [of] and host Syrian refugees and others that are fleeing from war."

Brende also pitched in, judging the minimum 120-day moratorium on receiving  refugees as "not up to our standards." He noted that the strongest opposition to the measure had come from Americans themselves, and that there had already been "backtracking" in the cases of green-card holders. "It shows there is checks and balances in a democracy," Brende said.

Analyst: Keep calm but ask questions

The director of foreign policy at the Center for European Reform, Ian Bond, suggests that Europe's first order of business is not to overreact - but that it should initiate formal diplomatic contact to find out just what the new policy will mean as the practical effects sink in.

"It is not unreasonable for the US to want to protect itself," Bond said in an interview with DW, "There is a terrorist threat and some of the countries on this list of seven are pretty much ungoverned spaces" where it would be hard ensure that a government, if it exists, has vetted people before issuing passports.

But it was not reasonable, Bond went on, to block would-be travelers who have passports from these countries plus EU passports. "I can't see any justification for that," he said. "If somebody has gone through the process that allows them to become a British citizen or a German citizen or whatever, then that should be good enough."

If the US was worried about some EU citizen in particular, he emphasized, authorities should take advantage of close law-enforcement cooperation to raise their concerns. Instead, he suggests, "This - potentially at least - is a great recruiting tool for 'Islamic State' and others of those ilk in the sense that they can say: 'We've always told you the Americans were anti-Muslim and now they've gone and proved it.'"

Given Trump's behavior, Bond suggests UK Prime Minister Teresa May's invitation for a state visit - filled with "ceremony and honor" - was premature. More than a million British citizens have signed a petition calling on Downing Street to retract the invitation, but the UK government says there'll be no cancellation.

EU leaders have also invited Trump for an EU-US summit at his earliest convenience and that, Bond thinks, should still take place, as even a "chilly" working session would give the two sides a chance to address their issues.  Besides, Bond points out, "you don't get a 21-gun salute from the EU or a carriage ride along the Rue de la Loi in Brussels." Given the state of affairs, he said, what the "EU ought to be doling out [to Trump] is more like what the military would call 'a meeting with no coffee.'"

Mogherini sent a veiled warning herself. In Europe "we celebrate when walls are brought down and bridges are built," she said, adding that the EU would continue its partnerships with all countries, regardless of their religions. "We have in Europe a history that has taught us that every time one invests in divisions and walls, you might end up being in a prison."