(Adds dollar figure in paragraph 1, byline)

By Hadeel Al Sayegh

DOHA, Sept 20 (Reuters) - Qatar's central bank sold 4.6 billion Qatar riyals ($1.26 billion) of conventional and Islamic government bonds on Tuesday in its second domestic government debt offer this year, suggesting liquidity is easing in a banking system pressured by low gas prices.

The central bank sold a total of 1.975 billion riyals of conventional bonds, including 450 million riyals of three-year bonds at a fixed rate of 2.25 percent, 775 million riyals of five-year debt at 2.75 percent, 500 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 2.625 billion riyals of sukuk.

The central bank only issued its first domestic bonds this year in August when it sold 4.6 billion riyals of conventional and Islamic government bonds.

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. ($1 = 3.6411 Qatar riyals)

(Writing by Tom Finn; Editing by David Clarke and Alexander Smith) ((Tom.Finn@thomsonreuters.com;))