Hamas launched several missiles toward Jerusalem but did not hit it. Israel shot down five rockets over Tel Aviv.
The Israeli military said there were 160 air raids on Gaza overnight in response to the rocket attacks.
The health ministry in Gaza says 25 Palestinians have been killed and 70 hurt in the recent hostilities.
The ministry said that four women and three children were among the dead.
The military wing of Hamas has warned that all Israelis are now targets.
Israeli General Moti Almoz said that a total of 430 targets in Gaza had now been attacked as part of "Operation Protective Edge".
He said that 120 concealed rocket launchers, 10 Hamas command and control centres and a number of tunnels had been hit.
Israel says that when it targets homes it telephones warnings to people inside to leave.
The BBC's Kevin Connolly in Jerusalem says rockets fired from Gaza reached the Jerusalem area in the hours before midnight, although they fell without causing injury.
Iron Dome interceptor missiles shot down five rockets around Tel Aviv on Wednesday morning, army radio said.
The town of Hadera 100km (60 miles) north of Gaza, was also attacked, with an M-302 surface-to-surface rocket, the furthest target so far reached.
"No other country lives under such a threat, and no country would accept such a threat," Prime Minister Benjamin Netanyahu said in a statement late on Tuesday.
"We have therefore significantly expanded our operations against Hamas and the other terrorist organisations in Gaza."
Israel has warned it may send ground troops into Gaza to stop the rocket attacks. It has authorised the call-up of up to 40,000 military reservists. Hundreds of reservists have already been drafted to bolster forces around Gaza.
Mark Regev, spokesman for Mr Netanyahu, admitted the situation was more one of escalation than de-escalation.
He told the BBC that efforts to try to calm the situation had failed as Hamas had continued to fire rockets, and the Israeli army was "now acting to put an end to this" by "dismantling Hamas's military machine".
"We don't want to have some sort of band-aid solution whereby we have a quick fix, a ceasefire and then we only have rockets on Israeli citizens next week," he said.
Palestinian Authority President Mahmoud Abbas demanded that Israel immediately stop the raids on Gaza and appealed for calm.
Among those killed in the Israeli raids were four Hamas members who died in Gaza City when their car was struck. One of the dead was Mohammed Shaaban, a senior militant.
Palestinian eyewitnesses also said that Hafez Hamad, a local leader of the Islamic Jihad militant group, was killed in an air strike in northern Gaza.
Later, the home of a Hamas leader in the southern city of Khan Younis was hit, killing six people. Health ministry spokesman Ashraf al-Qudra said two teenage boys were among those killed.
A Hamas spokesman condemned the air strike, calling it a "horrendous war crime".
Separately, the Israeli military released video footage that apparently showed Hamas militants emerging from the sea in diving gear on an Israeli beach before being killed by Israeli troops.
The government has declared a state of emergency in southern Israel.
In cities and towns within 40km of Gaza, summer camps and schools have been instructed to close and residents have been encouraged to stay near their homes.
The sudden escalation comes just days after suggestions of a truce from both Israel and militant groups in Gaza.
Tensions spiked last week with the murders of three young Israelis in the occupied West Bank and a Palestinian teenager in Jerusalem.
Israel says Hamas was behind the abduction and murder of the Israeli youths - a claim it denies.
A day after their funerals, the Palestinian was abducted in East Jerusalem and murdered. Police have arrested six Jewish suspects and say it seems the 16-year-old was killed because of his nationality.
Israel will press its air and ground offensive in the Gaza Strip, Prime Minister Benjamin Netanyahu said Monday, preparing his country for a longer and bloodier campaign and dashing hopes that the three-week-old conflict would end soon.
8 years, 2 months ago