Trump Jr. responded with a statement claiming the meeting was "primarily" about adoption and its relation to U.S. sanctions on Russian Federation under the Magnitsky Act.
Some advisers worry that Trump's action could spell legal jeopardy, the Post reported.
However, even as Sanders argued Trump was not being serious, the remarks from Trump prompted a furor of criticism from current and former law enforcement officers, police departments and civil rights groups, who claimed such words are unsafe in light of the current climate of distrust between police officers and the public.
"[Trump] refuses to sit still", the adviser added.
President Trump defended his habit of going on Twitter on Tuesday, saying it's the "only way for me to get the truth out!"
Alan Futerfas, one of Trump Jr.'s lawyers, repeated that statement to the Post Monday.
Press secretary Sarah Huckabee Sanders told reporters today that the president "has not" signed it, but "he will".
ForeignPolicy.com first reported Kushner's remarks.
At the time, one of Trump's top lawyers in the Russian Federation investigation, Jay Sekulow, told media outlets that the president "didn't sign off on anything" and "wasn't involved" in drafting the first Trump Jr. statement. The statement also said the subject of the meeting was not a campaign issue. "It came from Donald Trump Jr". Seventy-one percent say the president's tweets are hurting his agenda, according to the latest Fox News Poll.
Mr Trump Jr later acknowledged he had agreed to meet after being told Kremlin-linked information about Mrs Clinton would be offered during the talks.
Over the next three days, multiple accounts of the meeting were provided to the media as public pressure mounted, with Trump Jr. ultimately acknowledging that he had accepted the meeting after receiving an email promising damaging information about Hillary Clinton as part of a Russian government effort to help his father's campaign.
As it turned out, the Defense Department and key lawmakers who consider military issues were unaware of the policy shift and details of its implementation remain uncertain.
The comments seem to confirm that Trump participated in the drafting of the statement on Air Force One and contradict past statements from Trump's attorneys denying that he had any involvement.