Koch has campaigned for tough new measures to tackle youth crime, prompting a hostile reception from immigrant groups who have accused him of racism.
By early afternoon, 34.6 per cent of the 4.37 million eligible voters had cast ballots in Hesse, while only 22.65 per cent of the 6.1 million voters had turned out in Lower Saxony.
The elections come as Kurt Beck, SPD leader, looks to dismantle reforms brought in by Merkel's predecessor Gerhard Schroeder, a centrist Social Democrat.
Victory for the SPD would encourage them to push further for the introduction of a national minimum wage.
The mimimum wage proposal is popular with the German public but has been called potentially harmful to jobs by many economists.
Support for Koch has dropped by more than 10 per cent in the last few weeks, after he held a double-digit lead in the polls.
Koch recently called for tougher policies on young criminals from immigrant backgrounds, after a highly publicised attack on an elderly German man by two men, one Turkish, one Greek.
The strategy has been strongly criticised by immigrant organisations and Andrea Yspilanti, Koch's SPD opponent for the leadership of Hesse.
"You cannot put out a fire by pouring oil on it," a group of prominent members of Germany's 2.5-million strong Turkish community said in an advertising campaign in major newspapers.
Frank-Walter Steinmeier, Germany’s foreign minister and an SPD member, told Neuen Ruhr-Zeitung, a regional newspaper, that Koch's campaign could damage Germany’s image.
But Koch told Bunte magazine that the election "will help set the course for national politics … If we lose here it will be a problem for everyone."