Most daily newspapers did not appear on Friday, with the few exceptions including the right-wing Libero and Il Tempo and the smaller papers Il Foglio and Il Riformista.
Il Giornale, a large right-wing daily owned by Berlusconi's brother, also went on sale in spite of its editor's reservations about the law.
"We are not satisfied with the gag law," Vittorio Feltri, the editor-in-chief, said in a video message on Il Giornale's website, adding however that he found it "wrong to gag ourselves, losing the only means that allows us to speak to our readers".
The Italian senate approved the bill in June, which must now be passed by the lower house chamber of deputies and receive the signature of Giorgio Napolitano, the president, before becoming law.
One of the bill's provisions, heavily criticised by legal and police authorities, is the requirement that a three-judge panel approve successive three-day extensions to an initial 75-day warrant to wiretap conversations.
The bill also calls for fines of up to $590,000 for journalists or editors who publish transcripts of wiretaps in the media.
The measure exempts mafia and terrorism investigations from the restrictions.
The centre-right backs the measure as necessary for the protection of privacy, citing frequent leaks in the media of wiretap transcripts, notably involving Berlusconi himself.
Wiretaps are an important source for Italian newspapers, which last summer published transcripts of a purported recording of a call girl who claimed to have spent the night with Berlusconi.
More recently, they published a conversation between two businessmen the night of last year's deadly earthquake in Abruzzo laughing greedily over the moneymaking opportunity the destruction provided.
Angelino Alfano, the justice minister, who drafted the bill, has said there are more than 100,000 authorised taps each year.
At the time the bill was presented, Alfano said that this compared with 20,000 people wiretapped a year in France, 5,500 in Britain and 1,700 in the United States,
"In Italy, we are all spied on. There are 150,000 telephones that are tapped and it is intolerable," Berlusconi recently said.
International organisations have added their voices to the critics, including Reporters Without Borders, which denounced the proposed law as authoritarian.
In June, the Organisation for Security and Co-operation in Europe slammed the bill, saying it "could seriously hinder investigative journalism in Italy".
Last week, several thousand people rallied in Rome against the "gag law" in hopes that mounting public pressure might trigger changes to the bill during its passage in the lower house.
In the summer of 2007, journalists went on strike against a similar bill, proposed and then abandoned by the then centre-left government, calling for the ban on publication of wiretapped conversations obtained over the course of judicial investigations.