Financial Security Group Inc., the property and casualty insurance holding company owned by International Bank of Washington, reported a 6.3 percent increase in second-quarter profits yesterday and a 4.6 percent gain in earnings for the first half.

Financial Security's four insurance companies earned $2.9 million (96 cents a share) for the quarter, up from $2.7 million (89 cents) a year ago.

For the first half, Financial Security earned $4.7 million $1.58), up from $4.5 million ($1.51) a year earlier.

Investment profits contributed only $23,000 (on cent) to this year's first-half earnings but amounted to $358,000 (12 cents) a year ago. Underwriting profits fell to $1.5 million this year from $2.4 million for the 1978 half; the company sustained an underwriting loss of $57,000 in the first quarter, but eliminated that loss in the second three-month period.

Government Employees Financial Corp., the Denver-based consumer credit affiliate of Government Employes Insurance Co., reported lower profits for both the second quarter and first half and blamed higher interest rates.

Government Employes Financial said its net for the quarter fell to $697,000 (38 cents a share) from $750,000 (41 cents), and profit for the quarter was down to $1.42 million (77 cents) from $1.55 million (84 cents.)

Government Employes Financial officials noted that gross income for the first half was up 8 percent to $29.8 million from $19.2 million, but higher interest rates pushed up the cost of borrowings by 20 percent, costing the company more than $1.5 million in additional interest charges.

Scientific Time Sharing Corp. of Bethesda announced its net income fell by 17 percent to $980,000 from $1.18 million for its 1979 fiscal year ended May 31.

Revenues of the Maryland computer service company increased 23 percent to $16.6 million from $13.6 million.

STSC President Daniel Dyer blamed the downturn on higher-than-anticipated costs of the company's expansion into Europe. The European operation lost $927,000 last year compared with $153,000 a year earlier, and much of the European start-up costs are not eax deductible in the United States.

Virginia Real Estate Investment Trust reported a turnaround for the first half of 1979, earning a $251,000 profit (21 cents a share) this year compared with a loss of $43,000 (4 cents) last year.

Earnings for the second quarter were $116,000 (10 cents), up from a $107,000 (9-cent) loss.

The Richmond-based real estate investment trust also announced that Anheuser-Busch Inc. had exercised an option to buy 897 acres near Williamsburg for $1.6 million in cash.

The parcel was one of the trust's non-earning assets, and the sale reduced the amount of overdue loans from $4.5 million to $2.9 million.

Virginia REIT said it has agreed to give $1.3 million from the Williamsburg land sale and its interest in a 22-acre tract in Charlottesville to S. Douglas Fleet in exchange for 148,000 shares of the trust's stock. Fleet is a former trustee of the REIT.