Palestinian officials say a cease-fire with Israel has been agreed to by Hamas and Islamic Jihad.
The agreement, reached with the help of Egyptian mediation, was to take effect at 01:30 UTC. So far the cease-fire seems to be holding.
An exchange of rocket fire and airstrikes has killed four Israeli civilians and at least 20 Palestinians since Friday. These are the first Israeli civilian deaths from cross-border fighting since 2014.
President Donald Trump says the United States supports Israel 100% as it defends its citizens from Palestinian rocket attacks from Gaza.
"To the Gazan people -- these terrorist acts against Israel will bring you nothing but more misery. End the violence and work toward peace -- it can happen," Trump tweeted Sunday.
Israeli Prime Minister Benjamin Netanyahu has ordered the army to keep up "massive strikes" against Hamas targets in Gaza in the deadliest fighting along the border in five years.
Palestinian deaths include a 14-month-old baby and her aunt killed by what Hamas calls an Israeli strike. Israeli intelligence says a misfired Palestinian rocket killed them. Neither claim could be verified.
WATCH: Gaza violence
Palestinian militants have shot more than 600 rockets and other missiles into Israel since Friday. Israel says the smaller military group Islamic Jihad fired the rockets, but it holds Hamas, which controls Gaza, responsible.
The Israeli military says Palestinian militants have shot nearly 700 rockets from Gaza since Friday, and that Israeli forces have carried out strikes targeting 350 sites used by Hamas and Islamic Jihad.
Israel says the smaller military group Islamic Jihad fired the rockets, but it holds Hamas, which controls Gaza, responsible.
An Israeli airstrike also killed a Hamas commander, who Israel says was responsible for funneling money from Iran to the militants.
The current fighting was apparently sparked when an Islamic Jihad sniper wounded two Israeli soldiers Friday.
The Palestinians accuse Israel of failing to implement an Egyptian-brokered agreement to ease its blockade of Gaza in exchange for a halt in rocket attacks.
Hamas leader Ismail Haniyeh issued a statement late Sunday saying his militant group is "not interested in a new war" and says he is ready "to return to the state of calm" if Israel "immediately starts implementing understandings about a dignified life."
Israeli analyst Neri Zibler told I24 News that Netanyahu does not want a war with Hamas either.
"The greater good is to avoid needless wars. A war that you get into, you do not know how you will get out of it. A war that you go into and will most likely reach a conclusion and bring us back to the exact point we are in at the moment," he said.
A 50-day war between Israel and Hamas in 2014 killed more than 2,200 Palestinians and left entire neighborhoods in ruins.
The latest fighting comes on the eve of the Muslim holy month of Ramadan, and as Israel gets ready for Independence Day celebrations later this week.
Israel also hosts the eagerly awaited annual Eurovision song contest in Tel Aviv later this month.