BRUSSELS — A day after the departing president of the European Commission, Jean-Claude Juncker, dismissed the Brexit debacle as a “waste of time and energy,” European officials were confronted on Wednesday with the unpalatable task of deciding on yet another extension.

The European Union has already agreed to two Brexit extensions and the continued standoff in the British Parliament has forced the bloc’s leaders to consider granting a third, despite a mounting annoyance and exhaustion with the process.

On Tuesday, the British Parliament rejected Prime Minister Boris Johnson’s frantic efforts to compress the legislative timetable enough to allow the country to leave the European Union on Oct. 31.

Seeking a new deadline that seemed least likely to make a fuss, European officials were expected to settle on Jan. 31, the date set in British legislation passed recently. With an expedited procedure in place, the bloc could announce its decision by the end of the week.