The issue highlighted Netanyahu's reluctance to be seen as criticising Trump, who has expressed strong support for Israel and whose rise to the presidency was welcomed by the Israeli premier, some analysts said.
Netanyahu regularly speaks out against anti-Semitism in other countries, but the United States is Israel's most important ally, providing it with more than $3 billion per year in defence aid and important diplomatic backing.
Netanyahu had a testy relationship with Barack Obama, a Democrat who often pressured him over Israeli settlement building, but he has repeatedly praised Republican Trump.
So far, Netanyahu's only response to the weekend white supremacist rally in Charlottesville, Virginia that ended in bloodshed was a tweet on Tuesday that many saw as vague.
"Outraged by expressions of anti-Semitism, neo-Nazism and racism. Everyone should oppose this hatred," Netanyahu posted in English.
A Facebook post by Netanyahu's son Yair further raised eyebrows.
He denounced "neo-Nazi scum," but added that they were "dying out" and seemed to suggest left-wing counter-protesters "who hate my country" were a growing threat.
Criticism of Netanyahu among opposition politicians and others has grown louder over the last couple of days, particularly after Trump's comments on Tuesday in which he said there was "blame on both sides."
Perhaps the harshest criticism came from Shelly Yachimovich, a parliament member and former leader of the opposition Labour party.
"And you, the prime minister of the Jewish people in their land, the man who constantly warns us about a Holocaust, with excessive portions of fear and bombast and promises of 'never again,' what about you?" she wrote on Facebook.
"Was it too trivial, an anti-Semitic march in Charlottesville with Third Reich memorabilia?"
Former prime minister Ehud Barak, also from Labour, said "an Israeli leader should have said within six hours our position as Jews, as Israelis, as brothers of a large community, the American Jewish community, including in Charlottesville, who live under threat."
- 'Aren't two sides' -
Others issued more forceful denunciations of the rally than Netanyahu, including Education Minister Naftali Bennett.
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Opposition member Yair Lapid, head of the centrist Yesh Atid party, pointedly said in reference to Trump's comments that "there aren't two sides."
Israeli papers devoted front-page coverage to Trump's comments on Thursday, with top-selling paper Yedioth Ahronoth running a photo of him and the headline "shame."
Some commentators however pointed out that freesheet Israel Hayom, owned by Netanyahu and Trump backer Sheldon Adelson, buried the story deep inside the paper.
A spokesman for Netanyahu declined to comment on Thursday.
After Netanyahu's post on Tuesday, an Israeli official said on condition of anonymity that "the tweet is unequivocal and states his revulsion at the scenes of bigotry that the world has witnessed."
But for some, it has not been nearly enough.
Gideon Rahat of the Israel Democracy Institute think tank said the Israeli government should be expected to respond to such events as a state founded as a "safe haven" for Jews.
"You know we always have the Holocaust on our minds, so you take this and you see that Jews are attacked somewhere," Rahat said.
But he said of Netanyahu that "I think that his concerns are his relationship with Trump."
For Abraham Diskin, an emeritus political science professor at Jerusalem's Hebrew University, Netanyahu has no choice but to be "cautious."
"You have to choose your fights," he said.
"You cannot fight on every issue. You cannot clash with someone who is that important to Israel on issues like that."
Whether Netanyahu could see a wider political backlash at home over the issue is an open question.
For Rahat, denunciation of such anti-Semitism is part of the "consensus" in Israel and opposition figures "can clearly use it against" Netanyahu.
Diskin said however that he believed most Israelis would not focus on the issue for long.
"Altogether, I think the vast majority of people will not remember the issue a week from now," he said.