BRUSSELS—U. S. and European foreign ministers sharpened their focus on the Turkish government’s response to the weekend’s failed coup on Monday, voicing worry—and in some cases, criticism—over mass arrests by authorities in the last 48 hours.

Even as they moved swiftly to condemn the coup as events unfolded on Friday night and Saturday morning, EU officials were already concerned about President Recep Tayyip Erdogan’s response. Officials feared he could further close the space for democratic opposition in Turkey, a growing source of conflict between Ankara, on one hand, and Brussels and Washington, on the other.

For the EU especially, the events throw up a familiar dilemma. While they have voiced concerns about Mr. Erdogan’s growing grip on power and the undermining of an independent judiciary and press in the past, the desire to cooperate with the Turkish authorities on shared interests like fighting Islamic State and stemming migration have often trumped those worries.

For the U.S., Turkey remains a key partner in the North Atlantic Treaty Organization. After a brief closure of the airspace by Turkish officials Saturday, U.S. forces resumed use of a Turkish-U. S. air base to attack Islamic State militants.

Nonetheless, on Monday morning Johannes Hahn, the European Union’s chief for the bloc’s enlargement and neighborhood policy, described Mr. Erdogan’s response to the failed military coup as “exactly what we have feared.”