President Donald Trump departs for travel to Louisiana from the White House in Washington, U.S., May 14, 2019.

The Trump administration will continue efforts to put ask people in the 2020 census if they are U.S. citizens, Justice Department lawyers told a federal judge in a court filing Friday, two days after President Donald Trump contradicted officials who said the administration was dropping any such bid.

The filing came at the deadline set by a federal judge in Maryland for the government to say whether it would abandon its controversial quest to have the citizenship question in place for the upcoming census, or whether it would continue the legal battle.

The latest twist in the census citizenship question saga came a week after the Supreme Court effectively blocked the query from being asked next year.

While the government said its effort will continue, the filing had a pessmistic tone that underscored how much of a legal longshot the Justice Department is facing in seeking to justify the question in court.

The filing contained no explanation of how the Justice Department believes it can win that fight. But it left open the door that Commerce Secretary Wilbur Ross will adopt "a new rationale to include the citizenship question."

"The Department of Justice ... and Commerce have been asked to reevaluate all available options," the Justice Department filing said.

Those departments "have been instructed to examine whether there is a path forward, consistent with the Supreme Court's decision, that would allow for the inclusion of the citizenship question on the census," the filing said.

Neal Katyal, a Washington, D.C., lawyer, scoffed at the development in a Twitter post.

"This is an absurd filing," wrote Katyal, who previously served as acting solictor general of the United States, the attorney who argues for the government in cases before the Supreme Court.

"They don't even explain how their "re-evaluation" of census Q is possible after telling the Supreme Court 5 separate times (inc last week) that everything had to be decided by June 30," wrote Katyal.

Although the Supreme Court last sent the dispute back down to lower courts for possible further argument, the decision left the Trump administration very little time to meet its own deadline for including the citizenship question on printed copies of the census question sheet.

And the Justice Department noted Friday in its filing that if the Commerce Department comes up with "a new rationale" for putting the citizenship question on the census," the plaintiffs who had originally challenged the question "will be fully entitled to challenge that decision at that time."

That in turn would start a new cycle of court hearings that would make it very difficut, if not impossible, for a judge and appeals court to rule on the issue before the census starts being conducted.

The Justice Department told U.S. District Judge George Hazel of Maryland on Friday that "if a viable path forward is found" to legally justify the citizenship question, the department's current plan it to ask the Supreme Court for instructions "to govern further proceedings in order to simply and expedite the remaining litigation and provide clarity to the process going forward."

Government lawyers asked Hazel to postpone setting a schedule for the parties in the case to request and obtain evidence from each other about the origin of the citizenship question pending Commerce chief Ross's "new" decision about a rationale for the question, or whether he even ultimately will continue to seek its inclusion.

Hazel rejected that request.

"Given that time is of the essence ... the prudent course is to proceed with discovery," Hazel said in an order.

A lawyer for plaintiffs in the case did not immediately respond to CNBC's request for comment on the court filing.

On Tuesday, Ross and a Justice Department lawyer had said that that the Census Bureau was in the processs of printing the census questionnaire without the citizenship question.

But Trump threw that plan into confusion Wednesday with a Twitter post that 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.

Hours after that tweet, Justice Department lawyers told Hazel of Maryland that the department was trying to find "a legally available path" under the Supreme Court decision to add the question.

Hazel's court is one of three federal courts where opponents of the citizenship question were challenging the question's inclusion.

Justice lawyer Josh Gardner told Hazel that Trump's tweet contradicted what Gardner had told the judge the previous day about plans to omit the citizenship question from the 2020 census.

"What I told the court yesterday was absolutely my best understanding of the state of affairs," Gardner said. "The tweet this morning was the first I had heard of the president's position on this issue, just like the plaintiffs and Your Honor. "

"I do not have a deeper understanding of what that means at this juncture other than what the president has tweeted. But, obviously, as you can imagine, I am doing my absolute best to figure out what's going on."

Gardner also told the judge on Wednesday that "the Census Bureau is continuing with the process of printing the questionnaire without a citizenship question, and that process has not stopped."

Hazel gave government lawyers until Friday to say whether they planned to pursue a legal fight to put the question on the questionnaire.