They said the men talked about being ready to die for the jihadist cause and discussed being inspired by last week's attack in London that killed four people.
A fourth person, a minor, was also detained in overnight raids, a police statement said.
As many as three more Kosovars are under investigation over their ties to the group which has been under surveillance since a year ago.
D'Ippolito said a search of a Venice apartment showed the suspects were getting in physical shape and watching videos of Islamic extremists demonstrating how to carry out knife attacks. One had returned recently from Syria, he said. It wasn't just theory and dogma, ' d'Ippolito said of the wiretaps.
Raids were conducted at 12 addresses in the historic city centre to find the men.
The jihadists seemed to have been attempting to produce a bomb but they lacked the essential materials for building an explosive device, D'ippolito said.
He confirmed that police searched 12 sites in Venice's center, Mestre and nearby Treviso.
"We have monitored all their movements, all their contacts with the outside world and we were also able to monitor all their social media and PC traffic, everything they did to keep in contact and also to indoctrinate themselves", said the magistrate, Adelchi D'Ippolito.
However, he did not confirm a report in La Reppublica newspaper that one of the men was overhead suggesting an attack on the Rialto Bridge over the Grand Canal - a major global tourist draw.
Interior Minister Marco Minniti praised the police for what he called "an important success in our terrorism prevention effort".
The current bridge, an arched stone construction which dates from the late 16th century, is one of the best-known landmarks in the floating city and its walkways are frequently packed with tourists.
Italian police have detained three Kosovars and a minor in Venice on suspicion of being part of a Daesh cell and plotting a terror attack in Venice.