Interim National Party leader Dr Shane Reti believes its caucus will be selecting the next prime minister on Tuesday.
Former leader Judith Collins was ousted on Thursday after a dramatic 15 hours.
Bridges revealed on Thursday it related to a lewd comment he made in front of fellow National MP Jacqui Dean in 2017, which had been dealt with in-house at the time.
Reti, who was Collins' deputy, has taken temporary charge until a final decision on a permanent leader is made on Tuesday.
He refused to be drawn on Breakfast on Friday morning whether he would be running for the top position permanently or if he was backing any MP in particular.
Reti said he had not "pondered on leadership" and was "keeping an open mind" about it.
He said the future leader would possess inspiration and composure and would have "attention to things that matter to New Zealanders".
"On Tuesday, I'm of the view that we will be selecting the next prime minister."
Reti said his focus was on "shepherding caucus through until Tuesday".
According to 1News political editor Jessica Mutch McKay there are five candidates vying for leadership of the party — Bridges, Christopher Luxon, Mark Mitchell, Nicola Willis and Chris Bishop.
Reti remarked the potential list was 33 MPs and there was a "wide pool of talent to be drawn from" in the party.
He said he accepted and acknowledged the party had "plateaued a bit" in the wake of recent polls, but gave credit to Collins for "holding that line" of about 28 per cent.
Collins had "steadied the ship" following a "bruising" 2020 campaign, he said, denying the poll results reflected in-fighting. He admitted the party had made mistakes but would not detail what they were, saying "most of them are well known to the public".
Reti said the National Party was "credible", "legitimate" and a "Government in waiting".
1News political reporter Benedict Collins earlier told Breakfast Thursday's events had been an "absolute circus" with National's caucus in "open revolt" against Collins.
He remarked the "National Party circus just keeps on going" and said its MPs needed to stop "knifing and doing each other over".
This was a "massive turn-off for the public", Benedict Collins said, so the party needed to get behind a leader and "sort themselves out".