WASHINGTON — US Supreme Court Justice Anthony Kennedy issued a temporary order on Monday allowing the Trump administration to maintain its restrictive policy on refugees for the time being.

The order was in response to the administration’s request for the high court to block a lower court ruling that could allow up to 24,000 refugees to enter the United States.

Kennedy ordered challengers to the administration’s refugee ban to submit written arguments in support of the lower court ruling by midday Tuesday.

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The appellate ruling would allow refugees to enter the United States if a resettlement agency in the US had agreed to take them in. The ruling would have taken effect Tuesday without the high court’s intervention and could apply to up to 24,000 refugees.

The administration did not challenge the part of the ruling that applies to a temporary ban on visitors from six mostly Muslim countries. The appeals court ruled that grandparents and cousins of people already in the US cannot be excluded from the country under the travel ban.

The Supreme Court already has weighed in twice on lower court rulings striking down or limiting the travel and refugee bans, though it has to rule on their validity.

In June, the high court said the administration could not enforce the bans against people who have a “bona fide” relationship with people or entities in the United States. The justices declined to define the required relationships more precisely.

In July, the justices issued an order that temporarily allowed strict enforcement of the exclusion of refugees. But the Supreme Court refused to go along with the administration’s view that it could keep out grandparents, cousins and some other family members.

The 90-day travel ban affects visitors from Iran, Libya, Somalia, Sudan, Syria and Yemen.

The high court is scheduled to hear arguments about the legality of the travel and refugee bans in October. By that point, the original 90-day travel ban will have lapsed and the 120-day refugee ban will have just a few weeks to run. The administration has yet to say whether it plans to renew the exclusions, expand them or make them permanent.

The administration told the court Monday that changing the way it enforces the policy on refugees would allow “admission of refugees who have no connection to the United States independent of the refugee-admission process itself.”