The Israeli military said in a statement that it had “begun striking Hamas terror targets throughout the Gaza Strip.”
One position hit was a Hamas naval position west of Gaza City, and a another was a large Hamas training camp in northern Gaza, Palestinian security officials and Hamas media outlets said.
Both positions were likely to have been evacuated, as Hamas had hours of notice that Israeli strikes were coming.
Witnesses said three missiles hit the northern target. There were no immediate reports about casualties.
Israeli Prime Minister Benjamin Netanyahu had earlier promised a strong response to the rocket attack earlier in the day which injured seven Israelis, saying: “Israel will not tolerate this. I will not tolerate this. And as we speak Israel is responding forcefully to this wanton aggression.”
President Donald Trump signed a decree on Monday at the start of a meeting with Israeli Prime Minister Benjamin Netanyahu saying the United States recognizes Israeli sovereignty over the Golan Heights, territory that Israel seized from Syria in the 1967 Middle East war.
The decree formalized Trump’s statement on March 21 saying it was time for the United States “to fully recognize” Israeli sovereignty over the Golan.
The move appeared to give Netanyahu a boost ahead of the closely contested April 9 Israeli elections.
Mr Donald Trump said during his meeting with Mr Netanyahu that any future Middle East peace deal must account for Israel’s right to self-defense, shortly after the air strikes began.
Mr Netanyahu, who faces an election on April 9, cut his US visit short after the rocket fired from Gaza.
He arrived in Washington on Sunday, originally for a four-day visit.
Signing the document as Netanyahu looked over his shoulder, Trump said: “This was a long time in the making.”
He handed the pen that he used for his signature to Netanyahu, and said: “Give this to the people of Israel.”
Netanyahu welcomed Trump’s move and said Israel has never had a better friend. He harked back to two previous Middle Eastern wars as the reason why Israel needs to hang on to the Golan.
“Just as Israel stood tall in 1967, just as it stood tall in 1973, Israel stands tall today.
“We hold the high ground and we should never give it up.”
The rocket attack near Tel Aviv in central Israel, blamed on Hamas, came as the American Israel Public Affairs Committee (AIPAC), a pro-Israel group, held its annual meeting in Washington with speaker after speaker expressing U.S. support for strong ties with the country.
Israel’s Magen David Adom ambulance service said it treated seven people in the Israeli village, including an infant, a 3-year-old boy, a 12-year-old girl and a 60-year-old woman who was suffering from blast injuries, burns and shrapnel wounds.
The attack came as the American Israel Public Affairs Committee (AIPAC), a pro-Israel group, held its annual meeting in Washington with speaker after speaker expressing US support for strong ties with Israel.
Vice President Mike Pence said: “We stand with Israel because her cause is our cause, her values are our values, and her fight is our fight.”
Syria’s foreign ministry called the U.S. decision to recognise Israeli sovereignty over the Golan Heights a “blatant attack on the sovereignty and territorial integrity” of Syria on Monday, in a statement carried by state news agency SANA.
Russian Foreign Minister Sergei Lavrov has branded the move a violation of international law.
(More to follow)