The "two terror sites [were] in the central and southern Gaza Strip", the spokesman said. "Direct hits were confirmed."
He did not give further details
The new Palestinian government will have 17 ministers, five of them from Gaza, and will be headed by Rami Hamdallah who will also hold the interior portfolio.
Islamists Hamas and the Western-backed Palestine Liberation Organisation, which is dominated by president Mahmud Abbas's secular Fatah party, signed a surprise reconciliation agreement in April to end years of rivalry.
Since the start of the year about 150 rockets have rained on Israeli territory, but the border between Gaza and Israel has been relatively calm for the past weeks.
Palestinian militants fired the last rocket before the weekend attacks on May 23.