(Updates with details, background)

AMSTERDAM, May 13 (Reuters) - The Dutch government said on Friday it would pursue a stock market listing of insurer ASR (IPO-ASRN.AS), with an initial public offering of shares likely before the end of this quarter.

ASR, the country's fourth-largest insurer, had a book value at the end of 2015 of 3.57 billion euros ($4.1 billion).

The size of the offer and the pricing have not been determined and will depend on market conditions, ASR and NL Financial Investments, the agency that oversees it, said in a joint statement.

However in November, when the state first said it would likely seek to re-privatise ASR, the NLFI recommended selling a 30-50 percent stake.

The agency said in Friday's statement that the state will initially retain a "significant" portion of ASR's shares, but intends to sell the rest over time.

CEO Jos Baeten said the insurer is "looking forward to its new phase as a privatised business."

ASR, the insurance operations of the former Belgian financial group Fortis, was nationalised by the Dutch state together with ABN Amro during the 2008 financial crisis.

However, ASR's own financial stability was never in question. It is the Netherlands' largest disability insurer, and a major seller of property and casualty, funeral and health insurance.

In February, ASR reported a 25 percent rise in 2015 operating profit to 521 million euros ($580 million), and a solvency rating of 185 percent under Europe's new Solvency II regime.

It said on Friday it expects to be able to pay dividends as long as its solvency remains above 140 percent, with a payout ratio of around 50 percent of net operating result. ($1=0.8791 euros) (Reporting by Toby Sterling; Editing by Clarence Fernandez and Alexander Smith)