Several Remain-backing ministers were threatening to resign, so that they could vote for a cross-party amendment aimed at ruling out a no-deal Brexit, when MPs vote on a government motion on Wednesday.
Conservative Caroline Spelman and Labour's Jack Dromey said they "welcomed" the PM's statement but they would still table amendments paving the way for a bill to extend Article 50.
They will then "seek assurances from ministers during [the] debate to secure confirmation of the prime minister's commitments, which we hope will mean we will not push our amendments to a vote", the pair said in a joint statement.
Another of the MPs behind the amendment, Conservative Sir Oliver Letwin, had earlier said there was no need for it now, because the prime minister's statement "does what is needed to prevent a no-deal exit on 29 March".
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