Members of May's own party had urged her step aside — a move that would clear the way for a new Conservative leader to steer through the next phases of the U.K.'s departure from the EU.
Under a proposal, each EU member state would need to choose either "summertime" (daylight saving time) or "wintertime" (standard time). The change would go into effect in 2021.
European Union leaders gave the country two different deadlines, depending on whether U.K. lawmakers can agree on a path forward. One deadline is in two months; the other in two weeks.
Parliament approved a government plan to ask the European Union for an extension until June 30. European leaders will consider the request at a summit next week in Brussels.
The announcement Wednesday afternoon follows decisions by many other countries to ground the planes in the wake of Sunday's deadly crash of an Ethiopian Airlines flight.
Sunday's deadly crash of a Boeing 737 Max 8 in Ethiopia is spurring dozens of countries and airlines to ground the plane. In the U.S., the FAA is demanding design changes for the fleet.
The vote was the prime minister's second chance to gain approval of the terms she struck with the EU for the U.K.'s exit on March 29. Parliament will now vote on whether to leave without any deal.
Meant to increase security in Europe, the decision to implement a screening process was announced in 2018. But confusion arose after several media outlets labeled it a "visa."