"We will update the house on the publication and introduction of the Withdrawal Agreement Bill on our return from the Whitsun recess," said government official Mark Spencer, after saying that the original postponement was until 7 June.
The vote delay follows the outcry by a number of pro-Brexit political parties over the concessions offered by May in her latest version, the fourth, of the Brexit deal.
Politicians from her own party and the opposition have been calling for her resignation.
Members of the Conservatives' 1922 Committee met twice, and it was revealed that they held a no-confidence vote but kept the ballots sealed. The group can hold a no-confidence vote if the chairperson receives letters requesting a vote from 15 percent, or 47 of its own MPs.
Others in Theresa May's Conservative Party have left the vote behind and are actively campaigning for her job.
Even the prime minister's staunchest supporters are voting with their feet. Andrea Leadsom resigned as the government's representative in parliament late Wednesday.
"I no longer believe that our approach will deliver on the referendum results," Leadsom said in her resignation letter.
Although May thanked Leadsom for her service, she used the opportunity to push the issue of her Fourth Plan.
"I do not agree with you that the deal which we have negotiated with the European Union means that the United Kingdom will not become a sovereign country," May said.
Although she refused to meet ministers on Wednesday, her spokesperson said she would meet with ministers on Thursday.
May’s latest plan maps out a second referendum and what she called a “customs compromise” which would include MPs voting for a temporary customs union.
It would also lay out the requirement that the UK would need to replace the Northern Ireland backstop by 2020. If the backstop is accepted, then a bill will have to be drafted to ensure that Northern Ireland remains aligned with the UK and in the same customs territory.
May also said she would ensure workers were not worse off after Brexit and would reinforce environmental standards.
May is going ahead with her schedule as well, according to her spokesperson, who said she was looking forward to welcoming US President Donald Trump, due to begin his visit on 3 June.