Pennsylvania Attorney General Josh Shapiro claimed Mr Trump had said: “Sometimes it’s the reverse, to make people — or to make others — look bad.”
Mr Greenblatt labelled the suggestion “very concerning” and added: “We would benefit from a clarification.”
Nevertheless, Mr Greenblatt said his main concern was actions not words, given the current climate.
“My interest and priority is not what the president says or does but how do I solve that problem,” he said.
Since Mr Trump took office in January, America’s Jewish community has been repeatedly targeted by antisemites. Hundreds of bomb threats have been made to schools and community centres, as well as the ADL offices.
During the interview on Tuesday, Mr Greenblatt received a call to say the organisation had received four further bomb threats at its offices in New York, Washington DC, Boston and Atlanta.
“It’s uncertain times in somewhat uncharted waters for the US Jewish community,” he said.
“Vandalism and bomb threats directed towards the Jewish community isn’t exactly news, but what’s different is the pattern, the tempo and the intentionality.”
He described Juan Thompson, recently arrested over some of the threats, as “a deranged person”.
He added: “When you see attacks like this, intended to threaten our communities and individuals, copy cats and unhinged individuals see that and take inspiration.
“We have an environment in which extremists are emboldened because for months there was no forceful public rejection of them and their ideas.”
Within hours of the interview, White House press secretary Sean Spicer condemned the day’s bomb threats, which were also aimed at more schools and community centres.
Mr Greenblatt called for attention to be focused on the Jews on the ground across America who are at the sharp end of the threats and disruption.
“We go to work every day ready to fight to protect Jewish people, so it’s our expectation that we are on the front line. Not on the front line is a mum who drops her daughter off at pre-school or a dutiful son who brings his elderly father to a rehab programme, so it’s those people who feel it much worse than we do.”
Despite his criticisms, Mr Greenblatt recognises the Trump administration’s efforts to reassure US Jewry.
“We have a president of the USA with a Jewish son-in-law and a daughter who is Jewish by choice. They are shomrei Shabbat and his grandchildren go to a Jewish day school. We have never had, in the history of this country, a president with such an intimate relationship with Jewish people.”
He also commended the president’s address to a joint session of Congress which opened with a condemnation of antisemitism, as well vice-president Pence’s recent trip to Dachau.
“These are probably symbolic signs that should be celebrated and elevated because they are meaningful words,” he said.
“We hope the present administration will pivot from words to action and take concentrated measures to protect the Jewish community.”
Later on Tuesday, Mr Greenblatt spent around half an hour addressing the APPG, with MPs Michael Gove and Iain Duncan Smith present.
The group’s chairman Tom Tugendhat told the JC: “Mr Greenblatt has a very important and interesting voice, so it was great to have him come and talk about some of the lessons of the USA and how they can be applied to us.”
