Latest: Merkel aims "to win back" far-right voters, as exit polls show she heads for fourth term
Angela Merkel has conceded that "of course we would have preferred a better result, that's completely clear".
She noted that her party has been in power for 12 years and said the last four years have been "extremely challenging".
Alternative for Germany has been harshly critical of Mrs Merkel and her decision to let in large numbers of migrants in the last two years.
Mrs Merkel told her supporters that "we want to win back AfD voters" by solving the country's problems and addressing their concerns.
Supporters of the Alternative for Germany party broke out in cheers as polls indicated they had emerged as the third-strongest party in Germany's election, and co-leader Alexander Gauland vowed they would "change this country".
Mr Gauland promised supporters on Sunday that the party, known by its German initials AfD, would stay on the heels of the country's established parties.
Mr Gauland said "we will chase them. We will chase Merkel or whomever else".
"This is a great day in the history of our party, we are in parliament. We will change this country," he added.
Martin Schulz told Social Democrat supporters at party headquarters that "today is a difficult and bitter day". He added that "we have lost the federal election".
He said that the party had been successful as the junior partner in Mrs Merkel's outgoing coalition government, citing its introduction of a national minimum wage among other things. But he conceded that "we clearly didn't manage to maintain and expand our traditional voter base".
Leaders of the Social Democratic Party say they plan to go into opposition after their disappointing second-place finish in the election.
The Social Democrats have been Mrs Merkel's junior coalition partner for the last four years.
Their decision complicates things for Mrs Merkel, who will have to look to other parties to form a new government coalition.
The head of the Social Democrat's parliamentary caucus, Thomas Oppermann, and party deputy leader Manuela Schwesig both said immediately after the results the party would go into opposition.
Ms Schweisig said on ZDF television "for us it is very clear that the voters have given us the task of going ahead as the strongest party in opposition".
Chancellor Angela Merkel is set to lead Germany for a fourth term as exit polls showed her conservative bloc finished first in the country's election.
Polls conducted for public television channels ARD and ZDF suggested support for Ms Merkel's conservatives was between 32.5% and 33.5% in Sunday's vote.
They indicate challenger Martin Schulz's Social Democrats trailed in second place with between 20% and 21% support.
The polls also suggested that the anti-migrant, nationalist Alternative for Germany(AfD) party will enter the national parliament for the first time with 13-13.5% support.
This marks a significant fain for the AfD party.
The full result is expected later tonight.
