Palestinian officials said at least three people, including two militants, were killed by Israeli fire.
Palestinian militants have bombarded Israel with dozens of rockets and mortar shells while Israeli planes struck targets throughout the Gaza Strip in what appeared to be the most intense exchange of fire since a 2014 war.
Palestinian officials said at least three people, including two militants, were killed by Israeli fire and nine were wounded, and an Israeli air strike destroyed the ruling Hamas group's TV station.
In Israel, the national rescue service said at least seven people were wounded, including a 19-year-old soldier who was in critical condition.
The fighting, triggered by a botched undercover Israeli military raid in Gaza, cast doubt over recent understandings brokered by Egypt and UN officials to reduce tensions.
A day earlier, Israel's prime minister had defended the understandings, saying he was doing everything possible to avoid another war.
The UN said it was working with Egypt to broker a halt in the violence. "Rockets must STOP, restraint must be shown by all!" the UN Middle East envoy's office tweeted.
The undercover troops, apparently on a reconnaissance mission, were discovered several miles inside Gaza on Sunday, setting off a battle that left seven militants, including a Hamas commander, and an Israeli military officer dead.
Around sundown on Monday, militants launched 100 rockets in less than an hour, the most intense barrage since the 50-day war four years ago.
The rockets, which continued into the evening, lit up the skies of Gaza and set off air raid sirens throughout southern Israel.
The military said planes, helicopters and tanks had struck more than 30 militant targets, including military compounds, observation posts and weapons facilities.
It also said it targeted a squad that was launching rockets.
Lieutenant Colonel Jonathan Conricus, a military spokesman, said the army had sent additional infantry troops, rocket defence systems and intelligence units to the Gaza border.
"We continue to strike and retaliate against the military targets belonging to terrorist organisations in Gaza, and as for our intentions we will enhance these efforts as needed," he told reporters.
Late on Monday, an air strike destroyed the Gaza City headquarters of Hamas's Al Aqsa TV station.
Israel had fired warning shots ahead of the strike, prompting the station to halt programming and replace it with a logo. Minutes later, the air strike flattened the three-storey building and the station went black.
Hamas spokesman Fawzi Barhoum condemned the bombing as "a barbaric, brazen aggression". Ten minutes later, the station resumed broadcasts, airing pre-recorded national songs.
Israel said the station "broadcasts violent propaganda" and provides "operational messaging" to militants. A second air strike destroyed a five-storey office building that housed Hamas media offices. The strike also followed warning shots, and there were no reports of casualties.
Hamas and the smaller militant group Islamic Jihad said the rocket fire was revenge for Sunday night's Israeli incursion. Islamic Jihad spokesman Daoud Shehab said the groups wanted "the occupation and its supporters to know that the lives of our sons come with a price".
In all, 200 rockets were fired into Israel by mid-evening, the army said.
The Israeli military said it intercepted 60, and most of the others fell in open spaces, but rockets landed in the southern Israeli town of Sderot, setting off a large fire near a shopping centre. Another rocket landed near a factory, and several homes were hit in southern towns.
The military said a bus travelling near the border was struck by an anti-tank missile, critically wounding a 19-year-old soldier.
The strike set the bus on fire, sending a large plume of black smoke over the area. Lt Col Conricus said others were injured in the attack, but gave no further details.
Six other people were lightly wounded by shrapnel in various attacks, medical officials said.