* Commerzbank concludes capital increase
* Proceeds used to pay back part of state bailout
* 1.6 mln used to pay back Soffin, 750 mln for Allianz (Adds detail on distribution of proceeds)
FRANKFURT, May 29 (Reuters) - Commerzbank said it had completed a 2.5 billion euro ($3.2 billion) capital increase, in a move to repay part of a bailout given to Germany's second-largest lender in 2009.
The bank sold 556 million new shares to repay funds it owes to the German state and insurer Allianz. Germany's bank rescue fund Soffin will receive 1.6 billion euros and Allianz will get 750 million euros.
Commerzbank said 99.7 percent of the subscription rights were exercised with shares sold at 4.50 euros each. The subscription period ended on May 28.
After the share placement and the capital increase, Soffin's stake in the lender will be reduced to roughly 17 percent from 25 percent.
In a two-stage bail-out, the German government took a 25 percent stake in Commerzbank and also granted 16.4 billion euros in debt-equity hybrid instruments known as a silent participation.
Commerzbank has sought to entice investors despite warning that 2013 would be a year of transition for the bank, and posting a first quarter net loss of 94 million euros weighed down by a 493 million euro restructuring charge.
Earlier this week, state-owned Spanish lender Bankia saw its stock price tumble after issuing billions of new shares, with little hope of a quick recovery amid tough business conditions.