Israel pressed Hamas on Wednesday to rein in rocket-firing militants in the Gaza Strip after the most serious outbreak of cross-border hostilities since a ceasefire ended an eight-day war in November.

The Israeli military said two rockets fired from the Gaza Strip struck southern Israel on Wednesday, causing no casualties, hours after it launched its first air strikes in the Palestinian enclave in four months.

"Police here is ready. In fact, all of the southern district is ready for these isolated events. We know to deal with it in the best way possible. As of now were are ready for any possible scenario", said operations officer of Sderot police, superintendent Kfir Solomon, at the site of the rocket landing site.

Israeli planes had gone into action on Tuesday, targeting what the military described as "two extensive terror sites in the northern Gaza Strip", after three rockets were fired into Israel earlier that day, causing no casualties or damage.