WASHINGTON — Taking up another key aspect of President Donald Trump’s hard-line immigration agenda, the Supreme Court on Friday agreed to decide whether the administration has the authority to ban asylum claims at the southern border.

Although a federal judge ruled that the policy Trump enacted on the first day of his second term was unlawful, it has remained in effect while litigation continues.

The Supreme Court’s ruling, due before the end of June, will be the final word on the Trump administration’s sweeping assertion of presidential power over people trying to make asylum claims at the border, notwithstanding federal law enacted by Congress that lays out a procedure to do so.

The asylum dispute is the third significant case on Trump’s immigration policies that the court is considering, while the justices could take up other Trump-related cases in the coming months.

The ban stems from a proclamation the president issued Jan.…