WASHINGTON >> President Donald Trump today signed a new version of his controversial travel ban, aiming to withstand court challenges while still barring new visas for citizens from six Muslim-majority countries and shutting down the U.S. refugee program.

The revised travel order leaves Iraq off the list of banned countries but still affects would-be visitors from Iran, Syria, Somalia, Sudan, Yemen and Libya.

Trump privately signed the new order today while Homeland Security Secretary John Kelly, Secretary of State Rex Tillerson and Attorney General Jeff Sessions formally unveiled the new edict. The low-key rollout was a contrast to the first version of the order, signed in a high-profile ceremony at the Pentagon’s Hall of Heroes as Secretary of Defense James Mattis stood by Trump’s side.

White House Press Secretary Sean Spicer was not scheduled to hold an on-camera briefing today either, leading to the appearance that the president was distancing himself from the order, which was a signature issue during his campaign and the first days of his presidency. The order also risks being overshadowed by unsubstantiated accusations the president made over the weekend that former President Barack Obama had ordered the wiretapping of his phone during the campaign.

The original travel ban caused immediate panic and chaos at airports around the country as Homeland Security officials scrambled to interpret how it was to be implemented and travelers were detained before being sent back overseas or blocked from getting on airplanes abroad. The order quickly became the subject of several legal challenges and was ultimately put on hold last month by a federal judge in Washington state. That ruling was upheld by a federal appeals court.

The revised order is narrower and specifies that a 90-day ban on people from the six countries does not apply to those who already have valid visas or people with U.S. green cards.

The White House dropped Iraq from the list of targeted countries following pressure from the Pentagon and State Department, which had urged the White House to reconsider, given Iraq’s key role in fighting the Islamic State group. Syrian nationals are also no longer subjected to an indefinite ban, despite Trump’s instance as a candidate that Syrian refugees in particular posed a serious security threat to the United States.

In a call with reporters this morning, senior officials from Homeland Security and Justice Department said the travel ban was necessary to allow the government to review what more can be done to properly vet would-be visitors and refugees.

The officials said 300 people who arrived in the United States as refugees were currently under investigation as part of terrorism-related cases. The officials pointed to those cases as evidence of the need for the travel order, but refused repeated requests to address how many of those people were from the six banned countries or how long they have been in the United States.

A fact sheet describing the new order circulated before the new order was announced cites negotiations that resulted in Iraq agreeing to “increase cooperation with the U.S. government on the vetting of its citizens applying for a visa to travel to the United States.”

The mere existence of a fact sheet signaled that the White House was taking steps to improve the rollout of the reworked directive. The initial measure was hastily signed at the end of Trump’s first week in office, and the White House was roundly criticized for not providing lawmakers, Cabinet officials and others with information ahead of the signing.

Trump administration officials say that even with the changes, the goal of the new order is the same as the first: keeping would-be terrorists out of the United States while the government reviews the vetting system for refugees and visa applicants from certain parts of the world.

According to the fact sheet, the Department of Homeland Security will conduct a country-by-country review of the information the six targeted nations provide to the U.S. for visa and immigration decisions. Those countries will then have 50 days to comply with U.S. government requests to update or improve that information.

Additionally, Trump’s order suspends the entire U.S. refugee program for 120 days, though refugees already formally scheduled for travel by the State Department will be allowed entry. When the suspension is lifted, the number of refugees allowed into the U.S. will be capped at 50,000 for fiscal year 2017.

The new version also to removes language that would give priority to religious minorities. Critics had accused the administration of adding such language to help Christians get into the U.S. while excluding Muslims.

“I think people will see six or seven major points about this executive order that do clarify who was covered,” said presidential counselor Kellyanne Conway in an interview with Fox News Channel’s “Fox & Friends.”

She said the new order will not go into effect until March 16, despite earlier warnings from the president and his team that any delay in implementation would pose a national security risk, allowing dangerous people to flow into the country.

Legal experts say the new order addresses some of the constitutional concerns raised by a federal appeals court about the initial ban, but leaves room for more legal challenges.

“It’s much clearer about how it doesn’t apply to groups of immigrants with more clearly established constitutional rights,” said University of Texas law professor Stephen Vladeck. “That’s a really important step.”

Removing language that would give priority to religious minorities helps address concerns that the initial ban was discriminatory, but its continued focus on Muslim-majority countries leaves the appearance that the order is a “Muslim ban,” Vladeck said.

“There’s still going to be plenty of work for the courts to do,” he said.

Associated Press writer Alicia A. Caldwell and Sadie Gurman contributed to this report.