June 9 (Reuters) - Ukraine's grid operator Ukrenergo said it would impose hour-long power cuts throughout the country on Monday evening in connection demand exceeding agreed limits.

In a statement on Sunday on Telegram, Ukrenergo said the rolling cuts would apply to domestic and industrial customers and be in effect from 4 p.m. to 10 p.m. (1300 GMT to 1900 GMT).

The restrictions, it said, would not apply to "critical infrastructure" sites providing vital services.

Russia over the past two months has intensified attacks on the Ukrainian energy system, knocking out the bulk of thermal and hydropower generation capacity.

Prime Minister Denys Shmyhal has estimated that about 9 GW of energy-generating capacity has been lost since March.

Ukraine's government ordered all ministries and regional authorities last Friday to stop using air conditioning and switch off external lighting.

(Reporting by Will Dunham)