On Sunday, Israeli Prime Minister Benjamin Netanyahu announced in a televised speech that the bombings from Israel would continue in full force against Gaza and Hamas.
Early on Monday morning, the Israeli military carried out a series of new air strikes.
At least 80 airstrikes have been carried out in what is described as the heaviest air raids so far since the conflict flared up a week ago.
The attacks targeted several houses belonging to commanders in Hamas, according to the Israeli military.
There are no reports of injuries from the raids in Gaza yet.
A power line is said to have been hit, causing power outages in large parts of Gaza, according to the AP.
Israel: over 3,000 rockets fired from Gaza
Before that, alarm sirens had been heard over southern Israel.
Shortly after midnight, new rockets were fired from Gaza at the Israeli cities of Beersheba and Ashkelon.
According to the Israeli military, terrorist Hamas has fired more than 3,000 rockets since Monday.
The conflict is now in its second week.
Despite international pressure from the United States and the United Nations, among others, there is still no brightening in sight.
Monday's attacks come after a Sunday described by Palestinian authorities as the bloodiest day to date with more than 40 dead.
International leaders work for a ceasefire
From the United States, President Joe Biden has called for calm and says his government is working with both parties to quell the unrest in the Middle East.
"We also believe that Palestinians and Israelis deserve equal access to security and enjoy equal parts of freedom, prosperity and democracy," Biden said in a pre-recorded video of the Id al-Fitr holiday, which concludes Ramadan.
Egyptian President Abdel Fattah al-Sissi has said he is working hard to bring about a ceasefire between Hamas and Israel.