(CNN) Lawyers for the Department of Justice told a federal judge in Maryland Friday afternoon that the Trump administration will continue to explore options of adding a citizenship question to the 2020 census, but made no mention of a potential executive order being considered by the White House.

Judge George Hazel nevertheless ordered the government to begin producing details about how the citizenship issue was handled in a lawsuit brought by immigrant rights groups who argue it is discriminatory.

An administration official stressed that as of now the census will be printed without the citizenship question, though discussions are continuing about how to challenge last week's Supreme Court ruling blocking the Census Bureau from adding it to the questionnaire.

Earlier Friday, President Donald Trump said he is considering his options, which include an executive order or a potential addendum to the questionnaire that would allow the question to be added at a later date. Such a move could require the administration to provide a new justification for the addition of the question, following a Supreme Court ruling requiring a new rationale.

Trump, who has been increasingly frustrated over the issue, has been encouraging his lawyers and aides to find a way to include the disputed citizenship question and did not on Friday rule out the possibility of signing an executive order.

"It's one of the ways -- we have four or five ways we can do it," Trump told reporters earlier Friday on the White House lawn. "It's one of the ways that we're thinking about doing it very seriously."

In its court filing, the Justice Department said the administration continues to "reevaluate all available options."

The filing goes almost directly against Hazel's previous order to Justice to provide an answer on its plans, and instead attempted to pause the court action while the Justice Department considers its options.

Hazel will not allow a pause in the case. He responded Friday that the groups suing the Commerce Department will be allowed to collect more evidence regarding whether the agency's reason to add a citizenship question was to discriminate against non-citizens.

"Regardless of the justification Defendants may now find for a 'new' decision, discovery related to the origins of the question will remain relevant," Hazel wrote Friday. "Given that time is of the essence, therefore, the prudent course is to proceed with discovery."

The immigrant-rights groups can start collecting evidence as early as Friday, Hazel said, and have until Aug. 19 to ask questions of the Commerce Department and Justice Department. They also may depose five Commerce and Justice Department witnesses, Hazel said, though it's not clear yet who those might be.

In a separate court case over the citizenship question, the possible deposition of Commerce Secretary Wilbur Ross was a heated dispute that the Supreme Court ultimately stepped in to prevent last fall.

A parallel proceeding will continue in New York as well.

The Justice Department in its filing argued that schedule should be paused while lawyers search for a "new rationale for reinstating a citizenship question" -- a move made possible by the wording of the Supreme Court ruling, which left the door open for the administration to try again to add the controversial question.

Federal Judge Jesse Furman in Manhattan is considering the Trump administration's recent statements about still trying to add a citizenship question to the census at the direction of the President, despite a Supreme Court ruling.

The American Civil Liberties Union has asked Furman to stop the Commerce Department from adding any citizenship-like questions to the 2020 Census or changing it in any way, and Furman said he would hear arguments on its request on July 23.

Civil rights groups argue it could scare off legal immigrants and others from responding, leading to undercounts.

"The Trump administration repeatedly argued the census forms could not be altered after June 30," Dale Ho, director of the ACLU's Voting Rights Project, said in a statement. "They've now changed their tune because the Supreme Court ruled against them. They can't have it both ways. Trump's lawlessness will not go unanswered."

The plaintiffs in the case argued in their filing on Friday that their case should go ahead on schedule, saying the government could not erase questions about discriminatory intent "merely by pretending that the same or a similar decision is somehow 'new' or somehow cures the discriminatory intent that Plaintiffs have established as motivating the addition of the citizenship question to the 2020 census."

Moves by the Justice Department to satisfy Trump would mean that the administration would face daunting legal challenges and a tenuous timeline as it prepares for the decennial population survey, which is used to set electoral boundaries as well as to determine how government funding is distributed for an array of programs.

A legal adviser who has been involved with the discussions over the last several days with Trump administration officials on the citizenship question said that while the administration is considering its options, lawyers are drafting potential language for an executive order. The source stressed that other options are on the table, but that some outside advisers believe that an executive order could pass legal muster.

Earlier this week an administration official called that option unrealistic, but others are pushing for that option.

"I believe the Supreme Court will affirm the constitutional right of the President and commerce secretary to add the citizenship question to the 2020 census, in a 5-4 opinion authored by the chief justice of the United States," said J. Michael Luttig a former judge who has close ties to top players in the administration.

But critics say courts would be unlikely to agree. They contend that while the Census Act vests power in the commerce secretary to administer the census, the President has no constitutional authority to modify it.

The White House said late Thursday that the President was "looking at every option."

Trump threw the situation into disorder earlier this week when he tweeted he wouldn't give up the battle even after his Commerce Secretary Wilbur Ross announced the census forms would be printed without the question -- a move the President signed off on earlier in the week. The internal dispute has led the President to privately air frustrations at his 81-year-old commerce secretary.

Trump has been frustrated at Ross's handling of the census issue, according to two people with knowledge of the situation, believing he folded too easily after the Supreme Court ruled on the matter this week.

His frustrations with his commerce secretary started before the high court decision, believing the issue has been mishandled from the start. But in recent days he's told allies that Ross let him down.

At this point it does not appear that Ross will be dismissed, the two people said. But in speaking with advisers, Trump has bemoaned the Commerce Department and the Justice Department for "giving up," according to the people.

He has said that all of his options weren't explored before the announcement earlier this week that the printing would go forward.

The legal adviser who has been involved with the discussions says that when the Department of Justice went forward earlier in the week to say that a citizenship question would not be added to the census, the department got "ahead of itself." The source acknowledges that the White House was informed in some form of what DOJ lawyers would argue, but said that there was not "adequate communication."

The President remains in contact with outside advisers and is frustrated that the DOJ seemed to be throwing in the towel and has complained that Chief Justice John Roberts should be responsible for the failure to get the question on the census, not the President, according to the source. A continued legal effort, the source contended, might "force" Roberts to make a decision.

Trump has aired frustrations at Ross previously. Early in the administration, Trump kept berating him for his handling of China trade talks. He also complained that he fell asleep in meetings. But he's remained on good personal terms with his longtime friend

Trump has said publicly that asking census-takers their citizenship status should be a no-brainer. But opponents say it could deter minorities and immigrants, even those in the United States legally, from taking the survey. That, in turn, could skew electoral maps in favor of Republicans and reduce government assistance programs for some communities.

At left, Attorney General William Barr, and, at right Commerce Secretary Wilbur Ross.

Trump is facing "limited options," according to a person familiar with the matter, that include a potential executive order or adding the question as a supplement with the upcoming census forms, which are already being printed.

Trump tweeted early Thursday that officials were working on the Independence Day holiday to resolve the issue.

"Department of Commerce and the Department of Justice are working very hard on this, even on the 4th of July!" the President wrote, before departing the White House for his Virginia golf club.

Trump's seemingly out-of-the-blue tweet on Wednesday reversing the administration's stance came as a surprise to the government lawyers tasked with arguing the case.

There was initially consensus among the White House and other top administration officials over the position the Justice Department would take -- that it would go ahead with preparing the census without a line asking "Is this person a citizen of the United States?"

But Trump changed his mind after a hearing Tuesday, according to a source familiar with discussions. Top Justice Department officials, including Attorney General Bill Barr, became aware of the pivot before Trump tweeted about it, but lower level attorneys at the Justice Department, including the lawyers who were due in front of a federal judge in Maryland on Wednesday, were not aware of the shift.

The legal adviser who has been involved with the discussions with the Trump administration officials told CNN the President is committed to showing leadership on the issue, adding, "The President has made clear he wants to fight."

This story has been updated with additional developments Friday.