ISTANBUL/MUNICH (Reuters) - German insurer Allianz SE (ALVG.DE: Quote, Profile, Research) is paying nearly $600 million to raise its stake in two Turkish insurers to a majority, bolstering its position in Turkey's fast-growing and under-insured market.

Allianz and Turkish conglomerate Koc Holding KCHOL.IS said on Monday they had signed an agreement allowing Allianz to raise its stake in Koc Allianz Sigorta AS to 84.2 percent from 37.1 percent.

Allianz is paying 248 million euros ($393.5 million) for the 47.1 percent stake in Koc Allianz Sigorta, Turkey's third-biggest non-life insurer, with a market share of around 9 percent.

In addition, Allianz is paying 125.2 million euros to raise its stake in life insurer Koch Allianz Hayat ve Emeklilik to 87 percent from 38 percent. The life insurer has a 5 percent market share, making it the country's ninth-biggest.

"The agreement strengthens our long-term commitment to the Turkish market, where we see a high potential for future growth," said Allianz board member Enrico Cucchiani in a statement.

Turkey's population of more than 70 million is relatively young and has a low penetration of insurance coverage. The country has been growing rapidly over the past five years.

Koc Holding, which also has interests in the energy, automotive and consumer goods sectors, said it was concentrating on becoming a stronger global player in selected sectors.

"In line with Koc Group's strategic decision to focus on a limited number of core sectors, we are happy to transfer our shares to our partner," Koc Chief Executive Bulent Bulgurlu said in the statement.

Japanese insurer Millea (8766.T: Quote, Profile, Research) holds stakes of around 10 percent in both insurers.