According to the reports, 3 Palestinians lost their lives in Gaza after Israel carried out dozens of air strikes in response to a barrage of rocket fire by extremists.
Gaza health officials said that a pregnant woman and her daughter, aged one, lost their lives in the Jaafari area. A Hamas militant also died in the north.
At least seven civilians were wounded by rocket fire in southern Israel.
The violence came as the UN and Egypt tried to broker a ceasefire between Israel and Hamas, which dominates Gaza.
UN Middle East envoy Nickolay Mladenov said he was "deeply alarmed".
"Our collective efforts have prevented the situation from exploding until now. If the current escalation, however, is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people," he warned.