"It is not her intention to lead the party in the 2022 general election," Solicitor General Robert Buckland told the BBC after the meeting. "Quite rightly she is focusing on the here and now and the need for Brexit to be delivered."
MPs and ministers rallied round May after the confidence vote was announced on Wednesday morning, sending the pound rising amid expectations she would win.
In a defiant statement earlier outside her Downing Street office beforehand, the prime minister said she was "ready to finish the job" by taking Britain out of the European Union next March. She warned that ousting her now, sparking a weeks-long leadership contest, would "create uncertainty when we can least afford it".
May also warned that finding a successor – who would automatically become prime minister – "would mean either delaying or stopping Brexit".
Victory makes the prime minister immune from a further Conservative challenge for a year under parliamentary rules, but does not resolve her central problem – how to get divided MPs to agree to her Brexit deal.
She was forced to postpone this week's vote in the House of Commons on the text after admitting she faced a huge defeat, as her own MPs joined with opposition parties to reject it.
"The last thing our country needs right now is a Conservative party leadership election," Home Secretary Sajid Javid said in a tweet.
Finance minister Philip Hammond said May's victory would unite the party and "flush out the extremists".
May was informed of the challenge after returning late Tuesday from a tour of European capitals in an attempt to salvage her Brexit deal. She had promised MPs she would seek "assurances" about their concerns over a so-called "backstop" plan to keep open the border with Ireland.