Wauquiez was elected head of the centre-right Republicans on Sunday, running on a hard-right platform that has seen him accused of cosying up to far-right National Front (FN) voters.
Twenty-four hours later, Xavier Bertrand, a party heavyweight from the northern Pas-de-Calais region, quit the Republicans -- the first of a handful of politicians to walk out.
"I no longer recognise my political family, so I've decided to quit," Bertrand, a moderate who served as the party's secretary-general from 2007 to 2010, said Monday evening, accusing Wauquiez of "aggressiveness".
On Tuesday, the mayor of the northern town of Roubaix, Guillaume Delbar, followed suit, as did two other Bertrand loyalists in the north.
Explaining his decision, Delbar said: "I cannot stay in a party whose leader did not choose clearly between Emmanuel Macron and Marine Le Pen".
Delbar was referring to Wauquiez's refusal to endorse Macron over the FN leader in this year's presidential election after the Republicans candidate, Francois Fillon, was knocked out of the race.
Mainstream parties of the left and right have traditionally rallied around the FN's opponent in the final round of elections to block the far-right's path to power.
But Wauquiez, a 42-year-old devout Catholic who takes a tough line on immigration and security, stopped short of backing Macron, only calling on voters to "not vote for Marine Le Pen".
Celebrating his election as party chief on Sunday, Wauquiez vowed to lead a "renaissance" of the right.
'I need you'
He romped to victory over two little-known rivals, winning 75 percent of the votes cast by close to 100,000 party members.
But he faces a tough task to rebuild the once powerful party -- it changed its name from UMP to Republicans in 2015 -- which has lost millions of voters and several party heavyweights to Macron.
Analysts have said the only way the Republicans can survive Macron's centrist offensive is by tacking to the right to win voters from the FN -- at the risk of turning off more moderates.
On Tuesday, Wauquiez took a swipe at the departing Bertrand, saying it was "unacceptable to slam the door in this way".
But he also attempted to heal party divisions.
"Come as you are. I need you," he was quoted as telling Republicans lawmakers at a meeting, calling for "unity".
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![Ana Estrada suffered from polymyositis, an incurable disease that weakens muscles [Elias Alfageme/GDA via AP]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Ana Estrada suffered from polymyositis, an incurable disease that weakens muscles [Elias Alfageme/GDA via AP]")
