US president Donald Trump's administration is asking a federal appeals court to let his travel ban come into effect while it considers the case.
Attorneys for the president want the 4th US Circuit Court of Appeals to put on hold a lower court judge's ruling which blocked Mr Trump's revised travel ban targeting six predominantly Muslim countries while the court considers the merits of its appeal.
The administration said the people named in the case have not shown they will suffer "substantial harm" if the order takes effect. It also said the nationwide injunction blocking the ban is "fatally over-broad".
The Maryland ruling and a separate ruling in Hawaii blocking the ban were victories for civil liberties groups and advocates for immigrants and refugees.
The court, based in Richmond, Virginia, will hear arguments in the case on May 8.
Meanwhile, Hawaii is asking a judge to extend his order blocking Mr Trump's travel ban without holding another hearing.
US District Judge Derrick Watson temporarily halted the ban from taking effect, but his order is set to expire on Wednesday. That is when he has scheduled a hearing on Hawaii's request to block the ban until the state's lawsuit works its way through the courts.
Hawaii said in court documents that nothing has changed since Judge Watson ruled and a hearing is unnecessary. The state said that it will ensure the constitutional rights of Muslim citizens across the US are vindicated.
The Department of Justice said that if the judge grants the request, it should only cover the part of Mr Trump's executive order that suspends new visas for people from six Muslim-majority countries.