The Supreme Court could decide in the coming week whether to take up President Trump's travel ban.

The briefing schedule set by the high court ensures that the justices will be fully briefed on the fight before their term ends in June. The high court directed attorneys arguing against President Trump's travel ban to file briefs by Tuesday at noon and requested the Trump administration to do likewise by noon Wednesday.

The justices will enter their final scheduled conference on Thursday, which would mean they may make public any decision on whether to review the travel ban case on June 26, the final scheduled day for orders and opinions of the term.

Trump's Justice Department asked the Supreme Court to review the travel ban litigation and lift the blockades of the ban put in place by the 4th and 9th circuit courts of appeals. The litigation stems from a second executive order Trump issued to implement the ban. The second order looks to thwart nationals from six Muslim-majority countries — Iran, Libya, Somalia, Sudan, Syria and Yemen — from entering the U.S. for 90 days.

The justices could consider several factors as they decide whether to review the travel ban controversy. Some legal experts have argued that the travel ban via second executive order could become moot by the time arguments would begin if the Supreme Court chose to lift the blockades of the ban or because of the time elapsed from the original effective date of the order. The Trump team argued against the timing issue this week in its filings as the president issued a memo delaying the start date of the order.

Other court-watchers say Trump's tweets could become a factor in the justices' decision-making. After Trump tweeted his analysis of the travel ban and Justice Department's legal strategy this month, calling it a "watered down, politically correct" version of his original ban, attorney Brian Goldman tweeted that the president's tweets made him less confident the high court would take the case. Goldman works in Orrick's Supreme Court and appellate practice and formerly served as a clerk to Justice Sonia Sotomayor.

"[The] tweets are new, relevant evidence, but not part of the record in the case's interlocutory posture," Goldman tweeted.

"[The Supreme] Court may realize decision on the merits is a lose-lose," he continued. "Affirm, and the President will escalate war on the Judiciary. Reverse, and... the Pres. and others will act as if he's brought the courts to heel."

The 9th Circuit Court of Appeals mentioned Trump's June tweets in its opinion keeping the blockade of the ban, and attorneys for the state of Hawaii used the same tweets in its filings with the high court.

Trump's recent meeting with the nine justices also could play a role in shaping the justices' minds. Trump visited the Supreme Court for the first time as president on Thursday to witness the formal investiture of Justice Neil Gorsuch. He met and took photos with all of the nine justices, hours before a filing deadline that the high court set for the Trump administration in the travel ban litigation. The Justice Department filed the briefs requested before Trump's visit.

Trump's relationship with some of the justices has been fraught with controversy. Justice Ruth Bader Ginsburg, appointed by former President Bill Clinton, famously called Trump a " faker" during the 2016 presidential campaign. Trump responded to Ginsburg at the time in a tweet saying, "Her mind is shot — resign!"

Trump also has sharply criticized Chief Justice John Roberts, who was appointed by former President George W. Bush. During his presidential campaign, Trump referred to Roberts as an "absolute disaster" and a "disgrace."

Trump's visit to the high court came just after The Washington Post reported the president was under investigation for potentially obstructing justice in an FBI investigation. Trump appeared to confirm the investigation Friday in a tweet.

Such events could distract the Trump administration as the Justice Department prepares to argue in favor of the travel ban. Trump's pick for solicitor general, Noel Francisco, has advanced out of the Senate Judiciary Committee, but his nomination is still pending. Evidence of the Justice Department's rushing to meet deadlines appeared to be present in briefs filed last week, which included missing words.