In the run-up to federal elections next year, the Christian Democratic Union [CDU] has lost its absolute majority in Hamburg after a state election, according to exit polls.
The CDU, which is led by Angela Merkel, Germany's chancellor, will remain the largest party in the city-state after Sunday's vote but it saw its share of the vote fall.
Ole von Beust, the CDU's candidate, took 43 per cent of the vote, down 4.2 per cent from the last vote in Hamburg seven years ago.
The Social Democrats (SPD), which is part of a fractious "grand coaltion" with the CDU at the federal level, took 34 per cent, increasing its share by 3.5 per cent.
The Left party took 6.5 per cent of the vote, exit polls said, further signifying a voter swing to the left.
Should the exit polls bear out, the Left will win seats in Hamburg's legislature for the first time, echoing similar successes in state votes in Hesse and Lower Saxony last month.
As results emerged, the CDU confirmed that they were willing to set up a coalition in Hamburg with the Greens, who took 9.5 per cent of the vote, according to exit polls.
"This gives us the possibility to form a coalition either with the Greens or with the Social Democrats," Roland Pofalla, CDU secretary general, said.
"It is a good result that should be celebrated in Hamburg and in Berlin."
Should Beust decide on a coalition with the Green party, it could persuade Merkel to try a similar method at the federal level in 2009, when she will seek re-election.
The SPD is also considering new coalition partners in the run-up to the national vote in 2009.
The Left has become more popular after it emerged this month that hundreds of Germans deposited cash in secret accounts in Liechtenstein, in an attempt to evade taxes.
Kurt Beck, chairman of the SPD, has suggested that the SPD use Left party votes to seize power in Hesse after a deadlocked vote there in January.
Beck's idea was fiercely criticised by party members who are opposed to the Left, which is comprised of ex-communists and former SPD members.