The White House on Monday called the deaths of more than 50 Palestinians on the Gaza border "propaganda" by Hamas and denied that Israel was to blame.
And in an afternoon press briefing, the White House blamed the fatalities on the enclave's Islamist rulers Hamas.
Gaza's Health Ministry says the number of Palestinians killed by Israeli army fire near the Gaza border has reached 37.
Alexander quoted a statement from France's Foreign Minister Jean-Yves Le Drian calling on Israeli authorities "to exercise discernment and restraint in the use of force that must be strictly proportionate".
The White House said the Jewish state had the right to defend itself. "[But] we continue to implore Israel to show greater restraint".
"The PM said in December when the announcement was first made that we disagree with the USA decision to move its embassy to Jerusalem and recognize Jerusalem as the Israeli capital before a final status agreement".
Israel, for its part, has said the demonstrations are orchestrated by Hamas and has insisted its forces are acting "according to standard operating procedures".
Palestinian officials say Israeli military killed 55 people and wounded 2,700 in the deadliest violence in Gaza since 2014.