Spokesman Stephane Dujarric said in a statement on Friday: "The secretary general is deeply disturbed at the killing of civilians, including women and children, on a beach in Gaza earlier today."
He added that the UN chief "reminds all concerned of their obligations under international humanitarian law to avoid placing civilians in danger, while urging the utmost restraint to avoid further escalation and bloodshed."
THE US said it regretted the killings and welcomed Israel's decision to investigate.
White House spokesman Sean McCormack said in a statement: "We call on the Palestinian Authority to prevent all acts of terrorism including the firing of missiles and rockets from Gaza."
France described the killings as "disproportionate" and Moscow condemned them as "unacceptable".
Ten Palestinians were killed on Friday by the Israeli military.
- Seven people, including five members of the same family, died when an Israeli artillery shell reportedly landed on a Gaza beach.
- Three Palestinians were killed as they prepared to launch a rocket attack on Israel, the Israeli army said. Palestinians said they were civilians.
The deaths came following Israel's killing of a senior Palestinian militia member, Jamal Abu Samhadana, on Thursday.
Hamas has said it will end its 16-month agreement not to launch attacks on Israel in response to the incidents.