May told European Commission President Jean-Claude Juncker and German Chancellor Angela Merkel that the "government's planned timetable for notification of Article 50 remains unchanged", during separate phone calls, according to a statement released by Downing Street.
She added that the government was confident of winning next month's Supreme Court appeal against Thursday's High Court ruling that her government does not have the power on its own to trigger Article 50 of the Lisbon Treaty, which would formally start the process.
"The PM explained to both Chancellor Merkel and President Juncker that while the government was disappointed with the judgement, it had strong legal arguments ahead of the case moving to the Supreme Court," the statement said.
The decision raises the prospect of a protracted parliamentary debate before then -- in a chamber that overwhelmingly opposed Brexit -- although EU leaders themselves have urged a swift departure.
Lawmakers could also demand to know May's negotiating strategy and seek to maintain stronger ties with the bloc before agreeing to invoke Article 50.
Liberal Democrat MP Nick Clegg told BBC Radio Friday that he and other pro-EU lawmakers would "seek... to amend the legislation such that parliament would say to government it should pursue a soft Brexit, not a hard Brexit."
Bookmakers have slashed the odds of a general election early next year, three years ahead of schedule, as May could decide to expose obstructive anti-Brexit lawmakers to the pressure of public opinion and take advantage of her Conservative Party's huge polling lead.
In a sign of the likely parliamentary storms ahead, Conservative pro-Brexit lawmaker Stephen Phillips resigned as an MP on Friday, citing "irreconcilable policy differences with the current government".
The pound -- which has tumbled to multi-year lows since the referendum -- soared against the dollar and euro, standing at $1.2497 during afternoon trading in London.
Meanwhile, the White House urged Britain and the EU to "continue to be flexible and work this out in a process that is smooth, pragmatic, transparent and productive" following the court ruling.
The court's decision sparked fury among newspapers that backed Brexit, accusing the judges of "betraying" the 17.4 million people who voted to leave the EU.
The Daily Mail carried pictures of the three judges above a front-page headline reading "Enemies of the People", while its leading article called the ruling "a betrayal of common sense, the people and democracy".
The Sun editorial said in its editorial: "All our politicians... must ask themselves this: will they honour the biggest ballot box mandate in British history... or sniffily decide the little people cannot be trusted and thwart them?"
The pro-EU Guardian praised the judgement for putting parliament "back at the heart of the Brexit debate", but warned Remain supporters "not to get their hopes up" about its implications.
Most members of parliament wanted to stay in the EU, but commentators believe there is no majority support for reversing the referendum result.
The case challenged the government's right to use "historic prerogative powers" -- a type of executive privilege -- to trigger Article 50, which begins a two-year countdown to exiting the EU.
Robert Pigney, one of the claimants in the case, told AFP that the ruling was "an immense victory for the British people".
"It's very important that our elected representatives in parliament remain in control of our future," he said.
Nigel Farage, the interim leader of the UK Independence Party who led the Brexit campaign, urged May to call a general election and warned any lawmakers who attempted to delay Brexit had "no idea of the level of public anger they will provoke".
"The British people are not simply going to let this incredible establishment arrogance lie," he wrote in Friday's Daily Telegraph.
Opposition Labour leader Jeremy Corbyn, whose party opposed Brexit, said he respected the decision of the British people.
May has so far declined to outline her negotiating strategy, insisting that showing her hand would damage her chances of achieving the best outcome.
But she has indicated she will prioritise cutting immigration, a move that EU leaders have warned is incompatible with staying part of the European single market.