Complaints by passengers about the nation's airlines are continuing their decline, falling slightly last month from May and dramatically from June 1987, the Transportation Department says.

Monthly statistics released Thursday show that the department received 1,707 complaints about the airlines last month, down from 1,820 in May. The June figure was also 70 percent lower than the number of complaints logged during the same month a year earlier, when 5,774 gripes were registered.Statistics for the nation's 13 biggest airlines also showed that 80.5 percent of their flights into the 27 busiest airports landed on time, which means they landed within 15 minutes of their scheduled arrival.

Flights destined for Salt Lake City landed on time 91.9 percent of the time, the best percentage reported. Minneapolis, with an 86.5 percent on-time rate, rated seventh best and was the highest ranked city not in the South or West.

By contrast, the airports with the seven-lowest arrival rates were all from the Northeast: Pittsburgh, Philadelphia, Boston, Newark, N.J., both New York City airports, and Washington National Airport.

The department does not count flights that were late for mechanical reasons.

The statistics also showed that the airlines with the two highest on-time performances in May were carriers primarily serving the West and South: Southwest, with an on-time rate of 92.5, and America West, whose flights arrived as scheduled 90.9 percent of the time.

Pan American had the highest percentage of individual flights that were chronically late - that is, were late at least 70 percent of the time during May - at 6.3 percent.