At its national convention in Cologne, the Alternative for Germany party declined even to even consider a motion by Frauke Petry, the party’s co-chairman and its best known member, that called on the four-year-old party to seek to govern in coalition with other parties and to chart a more moderate political course.

The rejection was another blow to Ms. Petry. Last week, she had said she wouldn’t seek a spot on the AfD’s election ticket, a concession to other party officials who have rebelled against her leadership.

Instead, the AfD on Sunday chose a 76-year-old lawyer and former newspaper editor, Alexander Gauland, and a 38-year-old business consultant, Alice Weidel, to lead the ticket for the Sept. 24 national election, in which Chancellor Angela Merkel will stand for a fourth term.

Ms. Weidel is seen as a pro-business figure. Mr. Gauland, representing the party’s nationalist wing, is an ally of Björn Höcke, an AfD politician in the state of Thuringia whose rejection of Germany’s tradition of Holocaust remembrances stirred a nationwide backlash against the party in recent months.

Neither Ms. Weidel nor Mr. Gauland is as well known as the 41-year-old Ms. Petry, who has a doctorate in chemistry and is now pregnant with her fifth child. Analysts said that Ms. Petry’s leadership battles could hurt her party, which is already sagging in the polls. In an Infratest Dimap poll conducted last week, it received 10% support, a drop from 15% last fall.

“A party like the AfD does need to appear somewhat united,” said Thomas Poguntke, a political scientist at the Heinrich Heine University in Düsseldorf. “Permanent infighting is always bad.”

The AfD’s disunity is a contrast to France’s Marine Le Pen, who has successfully galvanized her National Front party around a message critical of immigration, Islam, and the European Union.

The AfD’s electoral platform, approved by delegates on Sunday, echoes that message.

It urges Germany to close its borders to asylum applicants, end sanctions on Russia and to leave the EU if Berlin fails to retrieve national sovereignty from Brussels, as well as to amend the country’s constitution to allow people born to non-German parents to have their German citizenship revoked if they commit serious crimes.

More than 10,000 people protested against the AfD in Cologne over the weekend, a city police spokesman said. Three of the 4,000 police officers mobilized to ensure security during the convention were injured, including one officer who intervened when an AfD delegate was attacked with a wooden plank, the spokesman said. Five people were detained.