TOKYO, June 27 (Reuters) - Japan's government said on Thursday its economy was gradually recovering, but warned in its monthly report that high interest rates in the United States and Europe risked damaging its own economy, as well as theirs.

A Cabinet Office official, who compiled the monthly report for June said these risks to Japan's economy included even more pressure on the weakened yen. The official declined to be named because he was not authorised to speak to the media.

The Japanese currency hovered above 160 yen overnight on Thursday, just a tad away from its low of 160.88 yen to the dollar, fuelling a concern about higher costs of living.

Sharp yen-weakening has raised a concern about the cost of living through surging import bills, which deals a blow to resources-poor Japan.

The yen has fallen some 2% for the month and 12% for the year due to stark interest rate differentials between the United States and Japan.

"The Japanese economy is recovering at a moderate pace, although it recently appears to be pausing," the report said.

"The economy could face downside risks from the effects of continued high interest rate levels in the United States and Europe," it added. "Full attentions should be given to fluctuations in the financial and capital markets."

By sub-sectors, the government retained its bleak views respectively for private consumption and exports - the two pillars of the economy - saying their pick-ups appear to be pausing.

Factory output has recently shown signs of a pick-up, the report said. It removed a reference to effects of some Japanese automakers that had falsified certification of some vehicle types since the beginning of this year. (Reporting by Tetsushi Kajimoto; editing by Miral Fahmy)