In the letter to her fractious colleagues, excerpts of which were released by Downing Street late Saturday, May urged the party to "move beyond what divides us".
The embattled British leader said ruling Tories need to sacrifice "personal preferences" for the "higher service of the national interest".
The plea came after May this week suffered another parliamentary defeat over Brexit, suggesting a shortlived period of party unity over reforming her draft EU divorce deal may not survive.
On Thursday night, MPs rejected a motion expressing support for May's efforts to seek changes to her under-fire agreement, after members of her own Conservative party abstained.
In her letter to lawmakers Saturday, the prime minister called the vote "disappointing" but insisted she would keep seeking to secure changes to the so-called backstop arrangement in the deal.
Her office revealed she planned "to speak to the leader of every EU member state in the coming days".
"I do not underestimate how deeply or how sincerely colleagues hold the views which they do on this important issue," May told Tories, referring to Brexit.
"But I believe that a failure to make the compromises necessary... will let down the people who sent us to represent them," she warned.
"Our party can do what it has done so often in the past: move beyond what divides us and come together behind what unites us."
May confirmed she would return to Brussels next week for further talks with European Commission President Jean-Claude Juncker.
Brexit Secretary Steve Barclay will on Monday meet EU chief negotiator Michel Barnier to discuss proposals put forward by a new "working group" of British lawmakers exploring alternatives to the backstop, according to her office.
Meanwhile Attorney General Geoffrey Cox will on Tuesday make a speech "setting out what changes would be required to eliminate the legal risk we could be trapped in backstop indefinitely", Downing Street said.
Britain is due to leave the EU on March 29, but its parliament last month rejected a draft divorce deal May negotiated with the bloc, prompting fears the country could crash out without a deal next month.