BRUSSELS—The European Union on Saturday launched legal action against Poland over part of the government’s planned overhaul of its court system, a move that could result in the government being fined and taken to the bloc’s top courts.

The EU’s executive arm, the European Commission, sent a letter to the Warsaw government formally raising concerns after a new law on the organization of the Polish court system was formally adopted on Friday.

The law is part of a package of measures pushed by Poland’s nationalist government that would have allowed the government to restaff the judicial bench, from the Supreme Court down to small, local courts.

On Wednesday, Brussels warned that the democratic rule of law remains at risk in Poland, even after President Andrzej Duda  vetoed government-pushed legislation that would have retired every high court judge.

Poland and the EU are in an extraordinary standoff over whether the former communist country can put virtually the entire judiciary under the control of the justice minister and remain a full-fledged member of the union.

Brussels could seek broader, unprecedented sanctions against Poland, although it is unlikely that would win sufficient backing from all EU member states.

While Mr. Duda vetoed the government’s effort to restaff the Supreme Court, he allowed through legislation that affects who sits in lower courts.

The commission said Saturday that this law breaches EU rules since it sets different retirement ages for male and female judges. More broadly, by giving the government the power to pick whose terms can be extended beyond retirement age, “the independence of Polish courts will be undermined,” it said in a statement.

Poland has a month to respond to recommendations that would bring Polish law back in line with EU norms. Failing that, the commission would move to the second of a three-stage infringement process that would end with Poland being taken to court.

A spokeswoman for the Polish Foreign Ministry didn’t respond to a request for comment Saturday.

European Commission First Vice President Frans Timmermans also wrote to the Polish government on Friday, inviting the foreign and justice ministers to Brussels to discuss the situation. In recent weeks, Warsaw has brushed off such requests.

The EU has limited room to maneuver in its broader rule-of-law showdown with Poland. The governing Law and Justice party says the reforms are needed to purge officials who entered public service during the tainted communist era. Previous warnings have done little to sway the government from its efforts.

The bloc’s most severe punishment—stripping a member country’s EU voting rights—requires unanimous backing from all member countries. But this is unlikely given Hungary’s support for the Polish government.

The fight is part of broader tensions between Brussels and some of the bloc’s newer members in Eastern Europe, which have increasingly chafed at the bloc’s policies and oversight. The EU has also raised a host of worries over legislation passed by Hungarian Prime Minister Viktor Orban.