The Prime Minister spoke to his counterpart yesterday afternoon after first telling MPs 24 hours earlier that he would speak to him "shortly".
Israeli media had reported that Mr Netanyahu was refusing to take calls from world leaders seeking to influence the response to Saturday night's barrage.
After the call, a Downing Street spokesperson said Mr Sunak "reiterated the UK's steadfast support for Israel's security and for wider regional stability".
They added: "Prime Minister Netanyahu thanked the UK for its rapid and robust support in the face of Iran's reckless and dangerous attack on Saturday.
'PM was deeply disappointed Hamas blocked a deal'
"The Prime Minister said Iran had badly miscalculated and was increasingly isolated on the global stage, with the G7 co-ordinating a diplomatic response. He stressed that significant escalation was in no one's interest and would only deepen insecurity in the Middle East. This was a moment for calm heads to prevail."
Mr Sunak also told the Israeli prime minister "he remained gravely concerned about the deepening humanitarian crisis" in Gaza.
His spokesperson added: "The UK wanted to see a massive step change in aid access to flood Gaza with vital supplies, including Israel opening up new aid routes as quickly as possible.
"The Prime Minister said it was deeply disappointing Hamas blocked a deal at the weekend that would have saved Palestinian lives and secured the safe release of hostages."
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