The US Supreme Court last Thursday blocked Trump's plan to add the citizenship question, saying administration officials had given a "contrived" rationale.
Administration officials including Ross said on Tuesday that the census forms were being printed without the citizenship question.
Critics have called the citizenship question a Republican ploy to scare immigrants into not taking part in the decennial population count and engineer an undercount in Democratic-leaning areas with high immigrant and Latino populations.
That would benefit non-Hispanic whites and help Trump's fellow Republicans gain seats in the US House of Representatives and state legislatures, the critics said.
"The News Reports about the Department of Commerce dropping its quest to put the Citizenship Question on the Census is incorrect or, to state it differently, FAKE! We are absolutely moving forward, as we must, because of the importance of the answer to this question," Trump wrote on Twitter.
Trump last Thursday also said he is exploring whether the census, which the US Constitution requires be carried out every 10 years, can be delayed.
But Ross, a key figure in the controversy, said in a statement on Tuesday, "The Census Bureau has started the process of printing the decennial questionnaires without the question."
At the same time, the Justice Department told a judge presiding over an ongoing court battle over the citizenship question that the administration had made a final decision not to proceed, according to two lawyers involved in the litigation.
Trump's administration had told the courts that its rationale for adding the question was to better enforce a law that protects the voting rights of racial minorities.
Critics called that rationale a pretext for partisan motives.
Although the Supreme Court left open the possibility of the administration adding the question in the future, there was little time left for the administration to come up with a new rationale.
The government had said in court filings that it needed to finalize the details of the questionnaire by the end of June.