ZURICH, June 10 (Reuters) - The Swiss National Bank (SNB) is ready to raise interest rates again as the fight against inflation continues, the chairman of the central bank said in an interview due to be published on Sunday.

SNB Chairman Thomas Jordan indicated that the bank was prepared to take further action in an interview with Swiss newspaper SonntagsZeitung ahead of the SNB's rates decision on June 22.

Swiss annual inflation dipped to 2.2% in May, data showed last week, but has remained above the 0.0-2.0% range targeted by the SNB since February 2022.

"The fight against inflation is not yet over," Jordan was quoted as saying. "We have to ensure that we bring it back below 2% on a sustainable basis.

"At this stage we cannot rule out a further tightening of monetary policy. We still have an environment where inflation is too high and is leading to relatively broad price increases."

Jordan has repeated his readiness to act in a series of recent public appearances and interviews ahead of the SNB's next rates meeting.

He said he would not be dissuaded from tightening policy even as increasing rents in Switzerland - linked to previous SNB interest rate increases - add to inflationary pressure. The SNB currently has a policy interest rate of 1.5%.

Although the SNB will take the development into account, it will not hold off fighting inflation because of it, Jordan said.

"Because then inflation would only increase even more, and we would have to raise interest rates more strongly with a time lag," he told the newspaper.

"This would be much more problematic for tenants. There is every reason to fight inflation as early as possible." (Reporting by John Revill Editing by Helen Popper)