Israeli army spokesman Jonathan Conricus said the "attack tunnels" detected were not yet operational. He declined to say how many were detected or how they would be cut off.
All operations would take place within Israeli territory, Conricus said, though they were likely to boost tensions with Hezbollah, the Shiite militant group with which Israel fought a devastating war in 2006.
The military has used various means to collapse or fill in tunnels from the Gaza Strip.
Netanyahu said he had planned to discuss with Pompeo "steps we are taking together to block the aggression of Iran and its proxies in the north," referring to Syria and Lebanon.
Hezbollah is backed by Iran, Israel's main enemy. (AFP) CPS
(With inputs from agencies.)