Two American members of the Israeli Defense Force have been killed in Gaza fighting, US media reported late Sunday, citing relatives and friends.

The State Department said two US citizens were killed in Gaza violence and released their names, but did not immediately disclose their occupations.

"We can confirm the deaths of US citizens Max Steinberg and Sean Carmeli in Gaza," spokesperson Jen Psaki said in a two-sentence statement.

"Out of respect for those affected by this, we have nothing further at this time."

Carmeli, 21, of Israeli parents, grew up in Texas, while Steinberg, 24, grew up in southern California, according to the Los Angeles Times.

Both were members of Israel Defense Forces' Golani Brigade, the Times said.

Steinberg, who lived in the city of Beersheba, joined the IDF in late 2012 and was a sniper in the brigade, according to the Jewish Journal of Greater Los Angeles.

The Israeli army said 13 soldiers were killed inside Gaza on Sunday, raising to 18 the number of troops killed since the ground operation began late on Thursday.

US President Barack Obama has called for an "immediate ceasefire" between Israel and Hamas, as the bloodiest day of fighting in Gaza raised the number of Palestinians killed to 501.

US Secretary of State John Kerry was flying to Cairo Monday for meetings with senior officials from Egypt and other countries.

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