WARSAW—Officials in Washington are putting pressure on Poland to end a constitutional crisis here or face a cooler patch in relations with the U.S., Polish officials said, in a sign of discord that could undermine Warsaw’s ambition to host more allied troops.

U.S. diplomats visiting Poland recently told government officials that they expected Poland to implement recommendations by Europe’s top international human-rights organization that Warsaw reverse its recent moves curtailing the power of the nation’s highest court to rule against government legislation. A draft opinion of the Venice Commission, an advisory body to the Council of Europe, sharply criticized those changes. The final version of the opinion is expected next week.

Since taking power in November, Poland’s right-leaning Law and Justice government has moved to install its judges at the Constitutional Tribunal, whose rulings on legislation are final. In doing so, the governing camp reversed appointments made in the previous term of parliament by its political rivals.

The move proved controversial and sparked public protests by opposition groups. It led to uncertainties over the legal status of the nominated judges, some of whom aren’t allowed to participate fully in the court’s work.

The governing camp then rewrote rules to make agreement by a larger proportion of judges necessary to pass rulings and to force the court to rule on cases in the order they arrive, preventing it from prioritizing them.