In a letter to European Council President Donald Tusk, May seeks an extension until June 30 and agreed to make contingency plans to take part in European Parliament elections in late May if necessary.
Tusk proposed a longer time frame. He urged the 27 remaining EU nations to offer the U.K. a flexible extension of up to a year to make sure the nation doesn't leave the bloc in a chaotic and costly way.
Two EU officials, who requested anonymity because they weren't authorized to disclose information before it was made public, said that Tusk wants a one-year "flextention" and hopes to get it approved at next Wednesday's EU summit.
Such a move would mean that the U.K. needs to take part in the May 23 to May 26 European elections, something which the U.K. prime minister has long argued would not be in either side's interest. The elections pose a substantial stumbling block because Britain would be expected to take part, if it is still an EU member, so its people have representation in the European Parliament. Officials worry the legitimacy of European institutions could be jeopardized if the population of a member state is not involved in the process.
Any extension to the deadline will need unanimous approval from the 27 remaining EU nations. French President Emmanuel Macron has thus far seemed cautious about giving Britain more time, saying the EU cannot be held hostage by Britain's political deadlock over Brexit.
If any EU nation refuses to back an extension, Britain will be expected to leave as scheduled on April 12. The complex maneuvering comes as Britain's Parliament considers legislation designed to prevent such a "no-deal" departure.
There are concerns that an abrupt exit without an agreed withdrawal deal could lead to economic slowdown and a breakdown in food and medical supplies as border checks and tariffs are added overnight. Massive traffic jams would also be expected on highways leading to major ferry ports as previously open borders were tightened with more identity and passport checks.
Britain's upper House of Lords is set to resume debate on the measure Monday. It was endorsed earlier by the lower House of Commons by just one vote. Despite the apparent support in Parliament for a new law to prevent a no-deal exit, the decision is in the EU's hands, not Britain's. Britain is the first country to try to leave the EU bloc, and the formal "Article 50" exit procedure has never been tested before.
EU leaders agreed late last month to prolong the Brexit date from March 29 until April 12, unless May could push their mutually agreed divorce deal through Parliament. The Europeans would prefer that Britain don't take part in the European Parliament elections if it is going to leave. April 12 is the last day for Britain to signal whether it will field candidates.
May said in her letter that Britain is reluctantly ready to begin preparations for the European elections if no Brexit deal is reached in the interim. She said she is making these preparations even though she believes it is not in Britain's interest or the EU's interest for Britain to take part in the elections because it is a departing member state.
May says she "accepts" the EU position that if Britain has not left the 28-nation bloc by May 23 it will have a legal obligation to take part in the elections. The prime minister says she is still hopeful of reaching a compromise agreement that could take Britain out of the EU before that time.
May says it is "frustrating" that Britain hasn't yet resolved the situation. Her withdrawal plan, agreed with the EU over more than two years of delicate negotiations, has been rejected by Parliament three times, leading to the current political and legal impasse.
She is now seeking a compromise in a series of talks with Labour Party leader Jeremy Corbyn and his deputies with hopes of winning opposition backing for a new divorce plans. If that doesn't work, May plans a series of votes in Parliament to see if a majority-backed plan can emerge.
Ideas being discussed include keeping Britain in a customs union with the EU after it leaves the bloc, as well as the possibility of a second referendum. There is fierce opposition from Conservative Party Brexit-backer to these options.
Britain voted by a 52% to 48% margin in 2016 to leave the bloc.
Raf Casert reported from Brussels. Lorne Cook contributed from Brussels.