The motion, proposed by a member of the far-right League party, declared the city “pro-life”. Under the scheme, pregnant women will be encouraged to give up unplanned babies for adoption.
The women marching in Saturday's protest will call for “safe and free” abortions on demand.
But the vote came just days before Pope Francis compared having an abortion to hiring a contract killer.
Right-wing mayor Federico Sboarina dismissed the row, saying the motion is “not anti-anything, but pro- : pro-life and the freedom of women”.
The measures would help women to “overcome the reasons, which can also be economic, which might lead them to terminate a pregnancy,” he said.
Italy's Family Minister Lorenzo Fontana, a League member himself, also backed the new measure. It did nothing more than apply the existing law, “helping a woman choose, so she can carry her baby to term”, he argued.
Forty years on, the law legalising abortion in Italy remains highly controversial, largely due to the sway of the powerful Catholic church.
Under the 1978 law, women can have abortions within the 90th day of their pregnancy, or within the 5th month for “therapeutic abortions”, induced if medically necessary.
Verona's new position is held up by critics as a symptom of a wider problem: the Roman Catholic church's influence on the country's health system, both in terms of its care structures and the training of doctors.
“We have an increasing number of hospitals that open their doors thanks to the financial support of the Vatican, while public hospitals have ever fewer resources,” gynaecologist and pro-abortion activist Elisabetta Canitano told AFP.
Private hospitals, especially ones funded by the church, can refuse to perform abortions.
She points to the Mater Olbia Hospital, a brand new facility located in Sardinia and owned by Qatar, and Rome's Gemelli Hospital, which is run by the Vatican. The Gemelli University Hospital Centre is also home to one of the most renowned medical schools in Italy.
“The church has always been interested in education and health, and when this generation of gynaecologists is gone, there will be no-one to replace them,” said Canitano, who works for the “Woman's Life” association that helps women with health issues.
Foreign women in particular — including refugees or prostitutes, often of African origin — are being forced into back-room abortions, she said.
“The situation is also serious for therapeutic abortions. We are bringing children into the world who we know will die, because 'it is God who gave it to you and God who takes it away',” Canitano said.
Italy has a very high number of conscientious objectors — practitioners who for moral, religious or personal reasons refuse to perform abortions.
Nationwide, 70 percent of practitioners took this position in 2016 — but that was as many as 90 percent in some southern regions, according to health ministry figures.
For the Association of Italian Catholic Doctors (AMCI) this right to opt out is sacrosanct, and it too has backed the Verona's council new stance.
Some 84,926 abortions were performed in 2016 in Italy, a figure steadily on the decline and nearly three times lower than the 1982 record.
But the AMCI says those headline figures do not tell the whole story: it estimates the number of drug-induced abortions performed in 2016 to be around 405,000, dubbing them “hidden abortions”.
It includes in these figures both the morning after pill, sold over the counter in Italy, and hospital-administered abortion pills.