Government Services Savings & Loan Inc. made a $6 million pretax profit on the sale of its Bethesda headquarters to The Artery Organization of Chevy Chase, the S&L reported yesterday in announcing earnings for the second quarter of its current fiscal year.

Earnings from the sale offset growing operational losses and enabled Government Services to post profits for the quarter ended Sept. 30 and the first half of the year, said President A.R.M. Boyle.

In a transaction completed during the latest quarter, Artery agreed to buy Government Services' facilities at 7200 Wisconsin Ave. for at least $11.3 million and possibly more.

Artery plans to ask to have the land rezoned so it can put up a building about three times the size of the one occupied by Government Services, Boyle explained. If the rezoning is approved, the value of the land will increase and Government Services will share in the gain, he said.

Boyle said he could not estimate how much more Government Services might get if the rezoning is approved, because that will depend on appraisals of the property's value two or three years from now.

For the latest three-month period, Government Services earned $1.74 million ($2.02 a share) compared with a loss of $474,000 in the same period a year ago.

Boyle said Government Services showed an after-tax loss of about $2.7 million for the quarter, but the real estate transaction produced an after-tax gain of $4.4 million.

For the first half of the year, Government Services earned $210,000 (25 cents) compared with a loss of $1.15 million during the first half of 1980.

Boyle said operating results for the quarter "were adversely affected by the continued unprecedented interest rate pressures," but rates appear to be going down now, forecasting improvements.