* Iceland c.bank cuts policy rate to 13 pct from 15.5 pct
* sees further "significant" cut in June
* more gradual pace of rate adjustment after June cut
* says progress being made toward easing capital controls
(Adds central bank governor quotes)
By Niklas Pollard and Mia Shanley
STOCKHOLM, May 7 (Reuters) - Iceland's central bank slashed its key interest rate by 2.5 percentage points to 13 percent on Thursday and forecast a further "significant" cut next month as the crisis-hit island nation's economy stabilised.
The Sedlabanki also said progress had been made toward easing the capital controls introduced last year to prop up the battered Icelandic currency though these were expected to be kept in place for "some time".
The bank's rate cut was the third easing in less than two months, a boon to the volcanic island's economy, which was devastated by the collapse of its banking sector and crown currency in October last year.
"The main concern we have is solidifying the balance sheets of households and companies," Governor Svein Harald Oygard told a news conference.
"I think the worst thing we can do is to create a situation where there is a risk for a further depreciation."
The central bank said "another significant adjustment of the policy rate" could be made at its June meeting, followed by "more gradual" easing of monetary policy.
Oygard said exchange rate stability was the bank's top priority.
"We do believe that a gradual approach is better. That will reduce the risk, and even create a situation where we can have an appreciation of the Icelandic kronor," he said.
Interest rates were pushed up six points to a record 18 percent last October, a condition set by the International Monetary Fund while it was cobbling together a financial rescue package that ultimately totalled more than $10 billion.
MORE THAN EXPECTED
The 2.5 percentage point cut was a little more than expected by the small number of banking analysts who cover Iceland after the bottom fell out of its economy. They said it was a sign that the bank believes inflation will continue to cool in coming months.
"The economy will be in need of as easy monetary policy as possible, under the condition that the exchange rate is not destabilised by rate cuts," said Mats Olausson, chief strategist for emerging markets at SEB.
The central bank is under pressure to aid the domestic economy through lower rates, but will be careful about cutting rates too quickly as it will also want to please the IMF, another analyst said.
But with inflation now falling, the central bank has moved quickly, reducing the cost of borrowing to 17 percent from a record 18 percent in mid-March and cutting by 150 basis points in early April at an extra monetary policy meeting.
Inflation was 11.9 percent in April, down from over 18 percent at the beginning of the year.
The central bank said the capital controls introduced to stabilise the economy and currency needed to be kept in place for some time to come.
"While current domestic and external circumstances do not yet allow for the dismantling of the capital controls without the risk of serious instability, there has been progress on several fronts that should allow the gradual, systematic easing of controls," it said.
Reuters monitors official statements on Iceland markets, companies and policy via the Internet from its Stockholm news room. (Editing by Patrick Graham)