May was facing a rebellion by up to 40 MPs from her Conservative party over an opposition motion which demanded she reveal her hand before triggering Article 50, the formal mechanism for leaving the EU.
In an amendment published today, May accepted the demand on the proviso that MPs "respect the wishes" of the June vote to leave the bloc and accept her timetable to trigger Article 50 by the end of March.
Up to 40 Conservative lawmakers had reportedly been planning to back the Labour motion in what could have been a symbolic blow against May's refusal to provide a "running commentary" on her Brexit strategy.
The government is currently fighting a legal challenge at the Supreme Court to stop parliament having the final say on a decision to trigger Article 50.
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Brexit supporters fear that MPs, who were overwhelmingly in favour of staying in the EU in the June referendum, might seek to delay the process or soften the terms of the break.
It also "confirms that there should be no disclosure of material that could be reasonably judged to damage the UK in any negotiations".
The government's amendment, published on Twitter by Conservative lawmaker Steve Baker, adds that "this House will respect the wishes of the United Kingdom as expressed in the referendum on 23 June".
It adds: "And further calls on the government to invoke Article 50 by 31 March 2017."
The motion and amendment will be subject to a debate and non-binding vote in the House of Commons tomorrow, although May will not be present as she is in Bahrain.
"We have always said we would come forth with more detail as we near the moment of triggering Article 50," she told AFP.