Leaders of the nationalist, anti-migrant Alternative for Germany (AfD) party have pledged to use their third-place election finish to conduct robust but "constructive" opposition, and sought to allay fears raised by Jewish groups and others about their entry into parliament.
However, long-running cracks at the top of the party widened when co-chairwoman Frauke Petry - one of AfD's best-known faces, but sidelined over recent months - stormed out of a press conference.
Ms Petry said: "An anarchic party ... can be successful in opposition, but it cannot make voters a credible offer for government."
She added that she would not join AfD's parliamentary caucus, and walked out of the room without taking questions.
Co-chairman Joerg Meuthen apologised "on behalf of the party" for the episode, saying it was "not discussed with us", before moving on.
Persistent leadership infighting so far has failed to cause the party significant harm.
Germany's mainstream parties have all ruled out teaming up with AfD, which is one of six caucuses in the new parliament after winning 12.6% of the vote. Including the seat Ms Petry won, it has 94 of the 709 seats.
Co-leader Alice Weidel told reporters the party's plan was to provide "constructive opposition".
She said: "We have a very clear mandate from the voters, and there is no time to waste."
AfD drew support from people who previously voted for Chancellor Angela Merkel's conservative bloc and from many who did not previously vote at all.
To a lesser extent, it also drained support from the centre-left Social Democrats and others.
Its success followed a campaign focused on criticism of the chancellor's decision to open the country's doors to more than one million asylum-seekers over the past two years.
AfD performed most strongly in Germany's formerly communist and less prosperous east, capturing 22.5% of the vote there - with 27% among male voters.
In the eastern town of Bautzen, which saw clashes last year between residents and migrants, Mrs Merkel's Christian Democratic Union (CDU) lost a seat it had held for more than 25 years to AfD, whose candidate received 32.8% of the vote.
Bautzen is located in Saxony, Ms Petry's home state and long an AfD stronghold. Across the state, AfD narrowly topped Mrs Merkel's CDU to become the strongest party, winning 27% of the vote.
Ms Petry turned AfD from opposing eurozone bailouts to a focus on migration after she ousted the party's founding leader in 2015, but has recently been sidelined after urging AfD to exclude members who express extremist views, with the aim of attracting moderate voters.
While she said she would not join the parliamentary group, she did not say she was leaving the party.
Co-leader Alexander Gauland sought to allay fears expressed by Jewish groups about his party's success. The Anti-Defamation League also called the AfD result a "disturbing milestone", saying "its leaders have made anti-Semitic statements and played down the evil of the Nazi regime".
Among other statements that have caused concern, AfD's leader in Thuringia state, Bernd Hoecke, called for a "U-turn" in the way Germany remembers its Nazi past, while Mr Gauland himself has repeatedly insisted "we have the right to be proud of the achievements of Germans soldiers in two world wars".
However, Mr Gauland insisted that "there is nothing in our party, in our program, that could disturb the Jewish people who live here in Germany."
He added that he had not met with Jewish leaders, but was "ready at any time" to do so.
He also dismissed concerns that AfD's rise was somehow linked to a wider swing to the right in Europe and the US.
French far-right leader Marine Le Pen and the Netherlands' Geert Wilders both were quick to congratulate AfD on entering parliament.
"I don't think that these parties are at all comparable, and that there is some kind of a mobilisation of nationalist parties across Europe," Mr Gauland said.
"Mr Trump has neither helped us nor hindered us, because we have different problems than the Americans, and Ms Le Pen's defeat in the end didn't hurt us because France has different problems."
He added that Austria's right-wing Freedom Party is "the only party where there is a closer relationship".