The day after MPs rejected the first attempt to call a snap poll, senior minister Jacob Rees-Mogg told MPs he would put forward a "motion relating to an early parliamentary election" to be voted on on Monday evening.
It would be put under a 2011 law that requires the support of two-thirds of the 650-seat House of Commons, Downing Street said.
A similar move on Wednesday night failed after the main opposition Labour party abstained.
Johnson called the election after MPs approved a bill that could undermine his threat to leave the European Union on October 31 without agreeing exit terms.
Labour said that while it wanted an election, it wanted the "no deal" bill passed first.
The bill is currently being debated in the unelected upper House of Lords but is expected to become law by Monday.
Government sources say they hope Labour would at that point back an election.
However, Labour is divided over the timing of any poll and could still oppose Johnson's motion on Monday.
Johnson wants a public vote before an EU summit on October 17, which could be the last chance to get a Brexit deal before Britain's scheduled departure on October 31.
But some in Labour want an election after October 31, which would force Johnson to delay Brexit, thus weakening his support among eurosceptic voters.
There is also the possibility that, if Johnson wins a majority in any early election, he would have the power to force through a "no deal" anyway.