Israel's military says its aircraft hit targets in Gaza after gunmen there fired a rocket at southern Israel.
No injuries were reported in the strike or the earlier attack from Gaza.
The military said Monday's rocket attack was the 18th since January.
Military spokesman Lt. Col. Peter Lerner says that "the intolerable reality of civilians continually living under the threat of Gaza rockets is unacceptable, unbearable and must stop. Hamas must enforce their responsibilities or face the consequences. We will act against those that attack us and hold those that enable attacks against Israel accountable."
A shadowy Gaza group, inspired by ISIS, claimed responsibility for the attack.
Israel holds the militant Islamic group Hamas that rules Gaza responsible for all attacks stemming from the territory.
Hamas said one of its training sites and other infrastructure were hit in the airstrikes.
Palestinian Authority President Mahmoud Abbas is seeking the help of the European Union to de-escalate the crisis with Israel, which he blamed on policies and actions of the Israeli government.
Before opening talks Monday evening with EU foreign policy chief Federica Mogherini in Brussels, Abbas told reporters the situation was "extremely serious and grave."
Abbas added, "It may even deteriorate, and that is my fear."
There have been almost daily Palestinian attacks against Israeli civilians and security forces.
In the past five weeks, 10 Israelis have been killed in Palestinian attacks, mostly stabbings, while 52 Palestinians have been killed by Israeli fire, including 30 said by Israel to be attackers and the rest in clashes.
A Palestinian hospital official says a Palestinian was shot and killed during clashes with Israeli forces in the West Bank.
Raed Said, a doctor at a hospital in Hebron said the Palestinian was pronounced dead on arrival Monday evening. He said he was killed in nearby clashes with Israeli soldiers.
The Israeli military said it was checking the claim.
Israelis are commemorating the 20th anniversary of the assassination of Prime Minister Yitzhak Rabin.
Rabin's daughter, Dalia, eulogized him at a ceremony at his graveside Monday and lamented that blood is still being shed two decades after the leader who sought peace was gunned down.
"I am not a bearer of good news today," she said. "there are no peace talks and there is terror and blood is spilling again and the impasse is growing and I have no other country and I don't recognize my country."
Rabin was shot dead after a peace rally on Nov. 4, 1995, by a Jewish extremist who wanted to stop the Oslo peace process Rabin initiated with the Palestinians.
This year's anniversary comes amid a fresh round of violence between the Palestinians and Israel.
The ceremony was attended by Prime Minister Benjamin Netanyahu, President Reuven Rivlin and other officials.
The Israeli army says its forces shot a Palestinian who tried to stab an Israeli soldier near a sensitive holy site in the West Bank city of Hebron.
The army would not elaborate on the condition of the Palestinian. The soldier was unharmed.
The army says the stabbing attack took place Monday near a site known to Jews as the Cave of the Patriarchs and to Muslims as the Ibrahimi Mosque, the traditional burial spot of the biblical Abraham and his family.
Earlier Monday, the Israeli military said a Palestinian stabbed and severely wounded an Israeli soldier near Hebron before being shot and killed.
An Israeli official says that Netanyahu has ordered a "review" of the status of certain Palestinian neighbourhoods of east Jerusalem — an effort that could affect the residency rights of tens of thousands of Palestinians.
The official says Netanyahu recently ordered the review of Jerusalem neighbourhoods that lie outside of Israel's West Bank separation barrier. One-third of the city's Palestinians, up to 100,000 people, live outside the barrier.
The review comes at a time of deadly unrest between Israelis and Palestinians, much of it in east Jersualem. The Israeli official said these neighbourhoods suffer from "lawlessness" and a "serious discussion" is needed. He spoke on condition of anonymity because he was discussing a closed meeting.
The vast majority of the city's Palestinians hold residency rights but not citizenship. Stripping them of residency would affect their ability to work and travel inside Israel and prevent them from accessing health care and social services.
Any Israeli attempt to remove residency rights would likely generate an international uproar.
Muslim religious officials in Jerusalem say that Israeli police have blocked them from installing security cameras at the city's most sensitive religious site, despite a new agreement to place the surveillance equipment there.
U.S. Secretary of State John Kerry announced over the weekend an agreement between Israel and Jordan to install security cameras at the hilltop compound that has been at the centre of weeks of unrest. Palestinians accuse Israel of trying to upset a delicate status quo at the site, which is revered by both Jews and Muslims.
Netanyahu has welcomed the plan, saying the cameras will prove that Israel is not doing anything wrong at the site.
But Azzam Khatib, director of the Islamic authority that oversees Muslim affairs at the site, said Monday that Israeli police prevented work crews from installing cameras at the entrance to the compound.
Israeli police had no immediate comment.
Israeli police say a stabbing in Tel Aviv was unrelated to the recent wave of Israeli-Palestinian violence.
Police spokeswoman Luba Samri says an Israeli soldier was "very lightly injured" in a stabbing in Jaffa, a largely Arab area of Tel Aviv. She says the stabbing was of a "criminal" nature.