A bill, which the Senate will start examining on Thursday, is the first to get to parliament.
If approved, the draft legislation will enable same-sex couples to commit themselves to one another before a state official, to take each other's names and, in certain circumstances, adopt each other's children and inherit each other's residual pension rights.
"The first time I marched with these slogans, it was 10 years ago, and I was pregnant. I hope this time it works," said bank worker Costanza Tantillo, who joined the Rome protest with her partner and their two children, nine-year-old Beatrice and Ludovico, four.
Two women who marched nearby held up a sign that read: "Stella and Paola, we've been together for 30 years and you still don't acknowledge us."
Protests had been planned for 90 towns and cities across Italy, under the slogan "Wake up Italy! It's time to be civil."
Opponents of the bill, in contrast, are planning a show of strength at a demonstration scheduled for January 30 in Rome's Circus Maximus.
Hundreds of thousands are expected to attend the self-styled "Family Day," organised by mainly Catholic groups under the battle cry of "Defend our Children".
Angelo Bagnasco, the chair of the Italian conference of bishops, has denounced the whole debate as a "grave and irresponsible distraction from the real problems of the country".
In the world of politics, dividing lines cut across party loyalties. A minority faction within the ruling Democratic Party supports junior coalition partner the New Centre Right (NCD) in opposing a reform championed by Prime Minister Matteo Renzi.
Renzi, who has allowed his allies a free vote on the "issue of conscience", can however count on backing from most of the opposition Five Star movement, left-wing fringe parties and even sections of Silvio Berlusconi's Forza Italia.
Most observers expect Renzi will get the bill adopted in the end.
- 'Historic day' -
According to Italian media, there were at least 7,000 demonstrators in Turin, 5,000 in Milan, thousands in Rome and Bologna, a thousand in Bari in the south, and hundreds in Naples and Venice among others.
"It is a historic day for this country, an immense protest that was fed by the desire and enthusiasm of a lot of people who hold the belief in equality close to their hearts," said Gabriele Piazzoni, the national secretary of Italy's biggest gay rights group, Arcigay.
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In what many saw as papal intervention in the debate, Pope Francis on Friday ruled out any form of union except Catholic marriage.
"What he said didn't surprise me, all he did was to repeat the church's anthropological viewpoint," said Andrea Rubera, a gay man who married a fellow homosexual in Canada.
They came to the demonstration with their three young children.
"But he chose to say this on the eve of the day when we took to the streets to defend the rights of our children to have a little security."