The third place is expected to go to either the far-left Linke (Left) party or the Greens who are both tied at 16.5 percent. The anti-migrant Alteranative fuer Deutschland (AfD) is projected to come fourth with 11.5 percent.
The turnout reached 53.1 percent as of 4 p.m. local time (14:00 GMT), exceeding by 7.1 percent the attendance registered during the previous state election five years ago, according to the electoral committee.
On Sunday, Berliners were electing 149 members to the state parliament. The election comes just two weeks after the AfD pushed the Christian Democrats into third place in the northeastern state of Mecklenburg-West Pomerania.