The Washington Post Co. reported yesterday that it had profits of $34.1 million ($2.61 per share) in the quarter ended June 30, a 26 percent increase over its earnings of $27.2 million ($1.94) in the comparable period of 1984.

The communications company, whose chief subsidiary is The Washington Post newspaper, said its second-quarter earnings include a $1.1 million after-tax gain from the sale of a minority interest it held in a cellular telephone operation in New England. The sale added 9 cents a share to second-quarter results.

For the first half of 1985, Post profits were up 63 percent to $59 million ($4.36), from $36.2 million ($2.57) in the first half of 1984.

The first half of 1985 includes one-time after-tax gains of $12 million, worth 90 cents a share. These included the New England sale, as well as sale of minority cellular interests in the Pacific Northwest and the sale of a portion of the Post Co.'s interest in Sportschannel -- a four-city cable television operation.

Second-quarter revenue was $284.3 million, up 11 percent from $256.1 million in the second quarter of 1984. Newspaper division revenue rose 10 percent in the second quarter. Television station revenue rose 16 percent. Newsweek magazine's revenue was up 2 percent in the second quarter and virtually flat for the first half of the year.

The company said the repurchase of about 1.2 million outstanding Class B shares at the end of April reduced interest income and increased interest expense.

The company financed the $135 million repurchase both by borrowing and by using its own resources.