The nation's airlines continued to carry record numbers of passengers in August, according to statistics released yesterday.

Not all the airlines have reported yet, but most of those that have said passenger traffic was at record levels:

Braniff International, crediting new routes and bargain fares, reported a 38.3 percent gain in passenger traffic in August, the fourth consecutive month the airline has experienced record increases.

American Airlines reported its third straight month of record traffic with a gain of 25.7 percent from August 1977.

Allegheny Airlines said August business was up 17 percent from last August, with 67.1 percent of the airline's seats filled compared with 60.1 percent in the same month of 1977.

United Airlines said its business rose 30.8 percent during August, the third month in a row it set a record for scheduled passenger growth and the seventh successive month of double-digit traffic growth. United said it also set a record for daily average passenger load factor - the percentage of seats occupied in scheduled service - during the jet era, filling 74.4 percent of its seats for the month.

United said the availability of low discount fares boosted seasonally high demand during the summer, but also noted that a portion of its traffic fains were the result of a strike against Northwest Airlines.

In addition, Southwest Airlines - a successful Texas carrier with new federal authority to operate in and out of Chicago's Midway Airport - reported its business was up 37 percent from a year ago. Western Airlines also reported a record month.

National Airlines - sought as a merger partner by both the regional Texas International Airlines and the international Pan American World Airways - reported that August traffic was up 30 percent over the same month of 1977, but that July was better.

In other airline developments:

Texas International announced it would out regular-coach fares by up to 66 percent on flights between Las Vegas and cities in Texas, Missouri, Louisiana and Arkansas on its new service which begins Sept. 28. The fare cuts are the deepest ever announced by a major U.S. airline for and interstate route, according to TXI, and take advantage of a recently announced Civil Aeronautics Board policy giving airlines new pricing freedom.

Braniff has just started serving the Dallas-Las Vegas route - one of the new TXI routes - but at higher fares, a TXI spokesman said.

Eastern Airlines announced it would cut regular coach fares in half on 14 of its very short routes. The fares - close to the prices charged on buses between some of the cities - apply on segments that are short-haul extensions of longer-range flights that originate elsewhere.

A passenger will be able to fly between Baltimore and Philadelphia or between New York and Philadelphia for $14. Seven of the routes are within Florida.

The CAB approved first-class and promotional fare increases on Trans World Airlines' transatlantic routes but rejected a request for a 5-percent increase in economy fares. TWA will be allowed to raise first-class fares by 5 percent and promotional fares by as much as 15 percent, effective Nov. 1.