The Israeli advance came as the US military hosted Israeli and Lebanese military representatives in Washington DC on Friday to pursue a US-brokered plan to forge peace between the two countries and disarm Iran-aligned Hezbollah.
The US talks also aim to reinforce an April 16 ceasefire that has failed to halt cross-border fighting, with Israeli warplanes pounding Lebanon's south and east and Hezbollah firing drones and rockets into Israel.
The military said this week it had expanded ground operations beyond a security zone its troops have occupied since April 16.
During a visit to the Israel-Lebanon border on Friday, Netanyahu said troops had pushed even further, past the Litani River that cuts east-west about 30km into southern Lebanon.
"Our forces have crossed the Litani and advanced to controlling positions," Netanyahu said in remarks to military personnel, according to excerpts released by his office.
"We are operating in Beirut, in the Bekaa (Valley), across the entire width of the front, and are dealing Hezbollah a crushing blow."
The Israeli conflict in Lebanon has been the most deadly spillover of the Iran war, with more than 1.2 million Lebanese displaced by Israeli strikes and evacuation orders since March 2, when Hezbollah fired at Israel in support of Iran.
Since then, Israeli strikes have pummelled Lebanon's south, east and its capital Beirut, killing more than 3200 people, according to Lebanon's health ministry.
Israel says 23 of its soldiers and four civilians have been killed over the same period.
Early in the fighting, Israel ordered people south of the Litani River to flee.
On Thursday, the military ordered people south of the Zahrani River - which lies about 10km north of the Litani - to flee as well, declaring the area a combat zone.
Commenting on advances by Israeli ground forces, Lebanese security sources said Israeli troops had crossed the Litani near the village of Zawtar al-Sharqiyah on Thursday but retreated to the southern bank of the river later in the day.
Ground forces crossed back over the Litani again on Friday, the sources said, saying it was not a major advance and that it took place at an eastern point on the Litani that sits close to the Israeli border.
Speaking with troops in Israel's northern command on Friday, Israeli military chief Eyal Zamir said troops would continue pursuing what he described as Hezbollah "launch squads" and their operators and commanders at every level.
"Wherever we identify a threat, we will strike it," he said, according to remarks released by the military.
