Among the dead were Hamas commanders Nour Baraka and Mohammad Al-Qarra, medical officials said.
Militants fired 200 rockets and mortars at Israel on Monday.
Israeli Prime Minister Benjamin Netanyahu has cut his trip to Paris for World War I commemorations short to return to Israel after the violence erupted along Israel's border with the Gaza Strip, a spokesperson said.
The dramatic escalation came as months of deadly unrest along the Gaza-Israel border had appeared to be calming, with Egyptian-led efforts to forge a long-term ceasefire and bring much-needed reprieve to the impoverished Palestinian enclave having seemed to finally be making headway.
Israel's military had not confirmed those details.
Gaza health ministry spokesman Ashraf al-Qudra said six Palestinians were killed.
The clashes prompted Israeli airstrikes and a salvo of rocket fire from Gaza toward Israel.
In the West Bank, Abbas angrily accused Israel and the USA of ganging up behind his back to entrench Hamas's control over Gaza.
In an apparent attempt to defuse tensions, Israel's chief military spokesman said the special forces had not been dispatched to assassinate Hamas commanders, a tactic that led to wider conflict in the past and which has largely been abandoned.
The Israeli military responded by dispatching fighter jets to strike "terror targets" throughout the Gaza Strip, in what was shaping up to be one of the most serious rounds of fighting since the devastating 2014 Gaza war.
At least seven Palestinians, including a Hamas military commander, were martyred and another seven injured late Sunday in an Israeli raid in southern Gaza Strip, said officials.
Seven Hamas terrorists, including two senior commanders, were killed in the assault.
Palestinian officials say Israeli forces fired at a group of Hamas men who were inside a passing auto.
Islamic Jihad spokesman Daoud Shehab said the groups made a decision to retaliate for the deadly Israeli incursion "so the occupation and its supporters know that the lives of our sons come with a price".
Defense Minister Avigdor Liberman mourned the death of the slain IDF soldier, only known as Lt. Col. M.
Air raid sirens continued to sound throughout southern Israel, as well as in nearby areas of the West Bank.
"Netanyahu says he wants to avoid a needless war and even facilitated a transfer of $15 million from Qatar to pay civil servants' salaries in Gaza".
Naftali Bennett, Netanyahu's education minister and right-wing rival, compared the cash flow to "protection money" paid to criminals.
Yesh Atid party chairman Yair Lapid praised IDF soldiers "who with with bravery and determination reminded Hamas and our other enemies that there is no place where will not find them".
At least 227 Palestinians have since been killed by Israeli fire, the majority shot during protests and clashes, while others died in tank fire or air strikes.
Palestinians inspect the remains of a vehicle that was destroyed in an Israeli air strike, in Khan Younis in the southern Gaza Strip November 12, 2018. It was not clear if the burst of violence would derail the arrangements which are aimed at preventing a further deterioration of conditions in Gaza, under blockade by Israel and Egypt since a 2007 Hamas takeover.
