The prime minister is continuing to face pressure from her own MPs to resign following her pledge of a "new deal" on Brexit.
It comes after Commons leader Andrea Leadsom stepped down on Wednesday night over the PM's Brexit policy.
Downing Street has announced she will be replaced by Treasury minister Mel Stride.
Several cabinet ministers have told the BBC that Mrs May cannot stay in her post.
Standing in for Mrs Leadsom, Mark Spencer told the Commons: "We will update the House on the publication and introduction of the Withdrawal Agreement Bill on our return from the Whitsun recess."
He added that the government planned to publish the bill in the first week of June.
"We had hoped to hold second reading on Friday 7 June," he added.
"At the moment, we have not secured agreement to this in the usual channels. Of course we will update the House when we return from recess."
On Wednesday, Theresa May told the Commons that the legislation would be published on Friday.
Second reading is when MPs get a first chance to debate legislation, before deciding whether it should proceed to detailed scrutiny.
Earlier, Foreign Secretary Jeremy Hunt said she would still be PM when President Trump visits the UK in early June.
Responding to a question after a speech at the National Cyber Security Centre, he said: "Theresa May will be prime minister to welcome him and rightly so."
It is possible for Mrs May to quit as Conservative leader before Mr Trump's visit, but continue as prime minister on a caretaker basis.
The US president is due to make a three-day state visit to the UK from 3 to 5 June.
Speaking after Mrs Leadsom's departure on Wednesday, Mrs May said she was "sorry to lose someone of [Mrs Leadsom's] passion, drive and sincerity".
On Wednesday night, Mrs Leadsom said Mrs May's new Brexit plan had "elements I cannot support, that aren't Brexit".
The minister had been due to appear in the Commons on Thursday to give a business statement to MPs.
The UK needs to pass a law to implement the withdrawal agreement - the part of the PM's Brexit deal which will take the country out of the EU - in UK law.
Mrs Leadsom was set to announce when the prime minister's Withdrawal Agreement Bill - the legislation needed to implement the agreement between the UK and EU - would be introduced to Parliament.
On Wednesday, members of the Conservatives' backbench 1922 Committee held a secret ballot on whether to change party rules, to allow the prime minister to face a vote of no confidence immediately.
Mrs May is due to meet the chairman of the committee, Sir Graham Brady, on Friday.
The results, in sealed envelopes, will be opened if Mrs May does not agree to stand down by 10 June.
Mrs May survived a no-confidence vote of Conservative MPs in December.Under existing rules, she cannot be challenged again until December this year.