Johnson made the comments while facing questions from parliament's senior Liaison Committee.
Lawmakers from his own Conservative Party asked Johnson to confirm he would not seek to call an election rather than resign if he lost a vote of confidence.
Asked by an opposition Labour Party lawmaker about a report that a delegation of his own cabinet ministers was preparing to tell him to resign, Johnson declined to comment.
Despite being all but fatally wounded and government resignations rising to more than 30, Johnson said he had a mandate from the 2019 election to press on.
A new confidence vote in Johnson will not be brought by his lawmakers until at least next week after the Conservative Party committee governing the rules agreed to elect a new executive before considering allowing one.
However, Johnson may still be forced to resign before next week if more members of his cabinet quit.
Johnson said he was having a “terrific" week despite a slew of resignations by key allies and growing calls for his resignation from his own Conservative Party lawmakers.
He made the comment when asked how his week was going by opposition Labour Party lawmaker Darren Jones during a parliamentary Liaison Committee session.
Asked whether housing minister Michael Gove had asked him to resign, Johnson said he was not “going to give a running commentary on politic events.”
The Daily Mail earlier reported that Gove, one of the most senior ministers in the British government, had told Johnson he must quit.
And on Wednesday Johnson sacked Gove, the BBC reported.
At least 32 British lawmakers, including finance minister Rishi Sunak, have left Johnson's government in less than 24 hours, saying the British leader no longer has their confidence and plunging his government into crisis.
The departures started on Tuesday evening with Health Secretary Sajid Javid quitting.
Sunak's resignation letter followed just nine minutes later.
The resignations follow a scandal over whether Johnson's office told the truth about sexual harassment allegations against a lawmaker.
Johnson survived a no-confidence vote from his fellow Conservative members of parliament last month after a series of other scandals but is now facing the biggest political crisis of his premiership.
The news comes as Johnson continues to defy pressure from senior ministers and a mounting rebellion within his party to quit on Wednesday, vowing to stay on as prime minister and fight off any attempts to oust him.
One encouraged him to make a dignified exit by setting his own timetable rather than face a confidence vote.