Mr Mladenov, who attended the meeting alongside Mike Huckabee, the US ambassador to Israel, is believed to have asked Mr Netanyahu for a 14-day cessation of air strikes, but without success.
Appearing to acknowledge the impasse, he posted on social media after meeting Mr Netanyahu: “Long day in Jerusalem, sitting down with Prime Minister Netanyahu and his team.
“This is the start of a hard phase and I have never pretended otherwise. Not much of what we do now is dramatic. It is slow, grinding and technical work.”
The White House has so far refrained from publicly criticising Mr Netanyahu for continuing the bombardment.
‘Mostly just talk in the air’
However, one Israeli defence official said: “The Americans are exerting tremendous pressure to move forward with Trump’s peace plan in the Gaza Strip.”
He added: “No target date has been set for entry and no clear date has been set for the entry of the multinational peace force either. In the meantime, it’s mostly just talk in the air.
“Nothing has been enshrined in documents.”
Israeli officials acknowledged that, as in the case of Lebanon, if Mr Trump decided to order Israel to cease its campaign in Gaza then it would ultimately have to comply.
The Board of Peace appeared to alter its language in Israel’s favour following the meeting with Mr Netanyahu.