In a press conference with Mr Netanyahu, Mr Hammond said he was convinced the current fighting had been sparked by Hamas rocket attacks on Israel.
Mr Netanyahu thanked the British government for its support and compared Israel’s situation to that of Britain during the Blitz.
But Mr Hammond also told Sky News: "As this campaign goes on and the civilian casualties in Gaza mount, western opinion is becoming more and more concerned and less and less sympathetic to Israel.
"That's simply a fact and I have to tell that to my Israeli counterparts."
He said Britain was “gravely concerned” by the number of deaths, which now total more than 750 Palestinians and Israelis.
Earlier, at the Knesset, the Foreign Secretary met Israel’s Opposition Leader Isaac Herzog and President-elect Reuven Rivlin.
Last night Mr Hammond rejected United Nations’ claims that Israel was guilty of committing war crimes.
