Marriott Corp. yesterday reported its second quarter profits jumped by 45 percent and said there is as yet no sign that gasoline shortages are hurting its restaurant and hotel businesses.

Marriott earned $17 million (45 cents a share) for the 12 weeks ended June 15, compared with profits of $11.8 million (31 cents) in the same period a year ago.

Total sales of the Bethesda-based food and lodging giant increased 24-6 percent to $353 million from $283 million.

"Excellent gains were reported in all our groups," said President J. W. Marriott Jr. "Demand for our services has been brisk . . . Marriott Hotels results continue to show strong gains."

Occupancy rates at the Marriott hotels and motels continued to run above last year, producing a 35 percent increase in sales and a 27 percent jump in profits.

Attendance at Marriott's Great American theme parks "was off slightly" but the customers who came spent more money, boosting sales by 11 percent and profits by 20 percent.

The quarter's sharp improvement in profits boosted Marriott's first half earnings to $28.7 million (76 cents) from $20.5 million (55 cents), a 40 percent gain. Sales increased 23 percent to $655.9 million from $533.2 million.

Chessie Systems Inc. blamed "a sudden surge in diesel fuel prices" and "an overall softening of the economy" for a slight downturn in its earnings for the second quarter. TThe Chessie reported profits of $37 million ($1.87 a share) for the three months ended June 30, compared with $37.6 million ($1.91) a year ago.

The railroad said shipments of motor vehicles, steel, lumber and paper were smaller than expected and traffic in coal, coke and iron ore was less than a year ago.

Last year's strike left the Chessie with a $29.3 million loss ($1.50) in the first half of 1978, compared with a $45.3 million profit for the same period this year. Revenues increased to $896 milliom from $702 million.