The New York Times is taking steps to deal with the fallout over its publication last week of an anti-Semitic cartoon, including new training for journalists and tighter editorial guidelines.

The prestigious daily apologised over the weekend amid criticism over the cartoon in its international edition depicting Israeli Prime Minister Benjamin Netanyahu as a guide dog wearing a Star of David collar and leading a blind Donald Trump wearing a yarmulke.

On Tuesday, a Times editorial also took issue with the cartoon, noting that "anti-Semitic imagery is particularly dangerous now."

One person was killed and three injured in a shooting at a synagogue in California over the weekend, an attack which came exactly six months after a shooting at a synagogue in Pittsburgh, Pennsylvania, which left 11 people dead. 

The Times blamed a "faulty" oversight process, and on Wednesday, publisher AG Sulzberger outlined steps to avert a recurrence.

Sulzberger said the newspaper had stopped running all syndicated cartoons, which are created by outside parties, and had canceled its contract with CartoonArts International, the group that provided the controversial image.

He said "disciplinary steps" would be taken for the production editor who selected the cartoon and additional oversight would be required in the future.

"We are updating our unconscious bias training to ensure it includes a direct focus on anti-Semitism," Sulzberger said in the memo, which was published in the newspaper.

"This episode is a reminder that all of us are custodians of our trust and credibility with readers... Though I've been assured there was no malice involved in this mistake, we fell far short of our standards and values in this case."

Simmering outrage

The weekend apology from the Times failed to quell criticism of the editorial lapse and prompted a demonstration by a few dozen protesters outside the newspaper's headquarters on Monday.

"Someone drew it, someone approved it. They should be fired," tweeted the Simon Wiesenthal Center, the organisation which researches anti-Semitism and the Holocaust.

French Nazi hunter Serge Klarsfeld told AFP this week the cartoon was "insulting."

"It is an anti-Semitic cartoon, that is to say that Jews are guiding the world and that corresponds to a stereotype very common among the far right, which one also finds on the far left," he said.

Jonathan Greenblatt, CEO of the Anti-Defamation League, said the cartoon was "anti-Semitic propaganda of the most vile sort," but welcomed the moves by the Times.

"This type of content normalises anti-Semitism by reinforcing tropes of Jewish control, and does so at a time when anti-Semitism is surging," Greenblatt said.

"We've been saying that the New York Times owes the Jewish community more than an apology. That's why we're glad to see the paper's leadership is taking action and following the recommendations we've made to them."

The cartoon prompted outrage from Israel's UN ambassador, who demanded that the Times hold accountable those responsible for publishing it.

Ambassador Danny Danon said the cartoon "could have been taken from the pages of Der Sturmer, the Nazi propaganda paper, and yet these actions have gone unpunished."

On the pages of the newspaper, contributing columnist Brett Stephens also lashed out at the decision to publish the cartoon.

"The Times has a longstanding Jewish problem, dating back to World War II, when it mostly buried news about the Holocaust, and continuing into the present day in the form of intensely adversarial coverage of Israel," Stephens wrote.

"The problem with the cartoon isn't that its publication was a willful act of anti-Semitism. It wasn't. The problem is that its publication was an astonishing act of ignorance of anti-Semitism."

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