Earlier in January, American officials said they did not believe Iran was yet racing for a weapon.
Israel described Mr Shadmani as the top operational commander of the Iranian armed forces and a close associate of Supreme Leader Ayatollah Ali Khamenei.
The Palestinian city of Khan Younis was targeted by intensive airstrikes overnight, as Israel pursued its ramped-up offensive across the Gaza Strip.
The originally planned withdrawal of Israeli troops from southern Lebanon within 60 days has been delayed.
He had been involved in a significant number of attacks on Israeli civilians and soldiers, as well as arms smuggling, the statement said.
The spokesman, Basim Alawadi, said on Monday in an official statement that Israel had blatantly violated Iraq’s airspace and sovereignty.
According to the army, the command centres were used to plan and carry out terrorist attacks against Israeli soldiers and the state of Israel.
Those killed were members of Hezbollah’s elite al-Radwan unit
The targets were reported to have included command centres, tunnel shafts and rocket-launching pads in the middle of residential areas in the Gaza Strip.
Meanwhile, the closure of major roads in southern Israel continued for the third day for fear of escalation with Gaza.
