BERLIN — Chancellor Angela Merkel’s center-right government said Wednesday that it would not try to ban a far-right political party deemed “racist, anti-Semitic and revisionist” by domestic intelligence, choosing instead to focus on combating neo-Nazi extremism through other channels.

The decision comes as Germany’s main political camps stake out their positions ahead of a general election in September, in which Ms. Merkel is seeking a third term in office. The chancellor’s main rivals, the center-left Social Democrats and the Greens, who control the upper house of Parliament, announced in December that they would seek to have the far-right National Democratic Party, or N.P.D., banned on grounds that it violated the Constitution.

A separate filing submitted by Ms. Merkel’s government, alongside the one from the upper house, or Bundesrat, would have given political weight to the argument but was not necessary for petitioning the Constitutional Court....