Trump's decision to drop plans for an executive order was first reported by ABC News.
The issue has produced a series of headaches for the Justice Department, as Trump has insisted on moving forward despite earlier statements by administration officials that census forms would be printed without a citizenship question.
The administration was still ironing out the details of the action, which was likely to be an executive order, one official told Reuters News Agency.
Judge Jesse Furman of the US District Court for the Southern District of NY on Tuesday denied the Department of Justice's (DOJ) notice of motion to withdraw as counsel on a case concerning the census citizenship question.
A Supreme Court ruling barred the question for now.
Barr said he has been in regular contact with Mr. Trump over the issue of the citizenship question.
The high court said last week the administration did not provide adequate grounds for adding the question and called the government's argument "contrived".
The House is also scheduling a vote on July 16 to hold Attorney General William Barr and Commerce Secretary Wilbur Ross in contempt of Congress for refusing to comply with subpoenas related to the oversight committee's investigation on the citizenship question.
"I agree with him that the Supreme Court decision was wrong", the attorney general told the left-leaning Associated Press after touring a federal prison in SC.
Trump has floated the reason that the question could be used in drawing congressional districts, something that has concerned one of his possible 2020 opponents. Sen.
The Census Bureau had stressed repeatedly that it could produce better citizenship data without adding the question to the decennial census, which had not been done since 1950.
Judge Furman gave the DOJ a second bite at this apple if they can concoct some good reasons to replace the legal team. How many people are there? Are they citizens, are they not citizens?
"We have a number of different avenues".
"I think that's a very different and much more hard case", Clement said while speaking on a Wednesday panel.
"We're thinking about doing that. Think of it: 15 to 20 billion dollars, and you're not allowed to ask them, are you a citizen?" he added.
Hazel noted that it is well within the authority of the U.S. Attorney General to decide which lawyers to put on a case, but emphasized that this does not mean everything argued up to this point will be forgotten.
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