In a series of early morning tweets on Monday, Trump urged the Justice Department to ask for an "expedited hearing" at the high court and seek a "much tougher version" of the order temporarily blocking entry to the US from six Muslim-majority countries. He called the courts, which have blocked two versions of the travel ban, "slow and political."
It's unclear whether the president has conveyed his requests to the Justice Department, which he oversees, in a forum other than Twitter. The Trump administration had denied in the past that the measure was a "travel ban," despite the language used by the president.
Last week, the Justice Department formally asked the Supreme Court to let a ban on visitors from six mostly Muslim countries and refugees from around the world be put in place. The high court is also being asked to uphold the constitutionality of the Trump travel policy, which lower courts have blocked because, they say, it shows anti-Muslim prejudice.
The directive that would go before the Supreme Court is a narrower version of the executive order the president signed during his first week in office. The second order removed Iraq from the list of banned countries. An indefinite halt to entry from Syrian refugees was replaced by a temporary pause.
Earlier Sunday, Trump had criticised London Mayor Sadiq Khan after he sought to reassure residents about a stepped-up police presence following the attack, the third in the country in the past three months. Trump argued in a Twitter post for leaders to "stop being politically correct" and to focus on "security for our people."
The mayor's spokesman said he was too busy to respond to Trump's "ill-informed" tweet.