At the heart of the matter is how the court might rule on Mr. Yoon’s impeachment. Six or more justices out of the nine-member court must vote in favor of impeachment to remove Mr. Yoon from office. The top court currently has only six justices, after three others retired earlier this year, meaning that the impeachment could be overturned with just one dissenting voice in Mr. Yoon’s trial.

The opposition had pushed for Mr. Han, as acting president, to sign off on nominees to fill the bench in the Constitutional Court. But Mr. Yoon’s governing party argued that only an elected president had the power to appoint justices.