BRUSSELS — The European Union is stepping up pressure on the United States to add more European countries to the list of those whose citizens can travel across the Atlantic without a visa, holding out the threat of requiring Americans to get visas for trips to Europe if Washington does not agree.

The European Commission is expected to consider on Tuesday whether to change the visa requirements for Americans if their government does not agree to include additional European Union member states — Bulgaria, Croatia, Cyprus, Poland and Romania — on the list of those entitled to visa-free travel.

In the case of Canada, the dispute concerns two of those countries, Romania and Bulgaria.

The escalating dispute comes at a time when Washington is especially concerned about security, in the aftermath of terrorist attacks in Europe and the presence of suspected terrorists in the flow of migrants to the Continent out of the Middle East. Should the commission decide to move toward imposing visa requirements, it could be a blow to trans-Atlantic relations just before a visit to Europe by President Obama and could complicate negotiations on other issues, including a proposed trade deal.

Right now, Americans and Canadians generally can travel to Europe for business and vacations without a visa. But the European Union is insisting that the United States abide by a timetable previously agreed upon among European authorities for adding the five European countries that are not already on the list of those allowed visa-free travel to the United States. The deadline for that change is next week, but no agreement had been reached Thursday evening.