DOHA, Aug 17 (Reuters) - Qatar's central bank sold 4.6 billion riyals ($1.26 billion) of conventional and Islamic government bonds on Tuesday in its first domestic government bond offer this year, a central bank official told Reuters on Wednesday.

The central bank sold a total of 3 billion riyals of conventional bonds, including 1.5 billion riyals of three-year bonds at a fixed rate of 2.25 percent, 1 billion riyals of five-year debt at 2.75 percent, 250 million riyals of seven-year debt at 3.25 percent and 250 million riyals of 10-year debt at 3.75 percent. In addition, it sold 1.6 billion riyals of sukuk.

"The demand was fine and most banks participated," said the official, who added that bids by banks for conventional bonds had exceeded the amount offered by 50 million riyals, and for sukuk by 2.4 billion riyals.

"It is a good sign and shows liquidity in the system is okay," he said, adding that another issue was possible next month. He did not elaborate.

Reduced state revenues due to low natural gas prices cut flows of new petrodollars into Qatar's banking system this year, pushing money rates up sharply and causing the central bank to cancel several monthly sales of short-term bills.

Since June, however, money rates have come off their highs and liquidity has improved somewhat along with a rise in government deposits at commercial banks.

(Reporting by Tom Finn; Editing by Andrew Torchia) ((Tom.Finn@thomsonreuters.com;))