Howard Mitchell, 77, who was the second music director of the National Symphony Orchestra from 1949 to 1970, died yesterday in the Ormond Beach (Fla.) Hospital, where he had been in intensive care for about six weeks.

The cause of death was announced as heart failure resulting from complications after abdominal surgery. Mr. Mitchell, a resident of Palm Coast, Fla., had suffered from congestive heart disease for several years.

During his 20 years as conductor of the National Symphony, he took the orchestra on its first foreign tours, greatly increased the number of its subscription concerts and involved it in some landmark recording projects. Under his direction, the National Symphony became one of the most traveled orchestras in the world, with extensive, regular tours of the United States as well as occasional foreign excursions.

Mr. Mitchell was associated with the National Symphony throughout his adult life. Born in Nebraska and raised in Sioux City, Iowa, he began to study the cello when he was 15. He joined the orchestra as its principal cellist in 1933 while he was still a student at the Curtis Institute in Philadelphia.

Mr. Mitchell made his conducting debut with the symphony in 1941 and was appointed the orchestra's assistant conductor that year. He was named associate conductor three years before taking the helm in 1949.

His greatest conducting challenge before assuming leadership of the orchestra was in the 1946-47 season when he stepped in to substitute for Hans Kindler, the orchestra's founder and first music director, on a few hours' notice after Kindler was taken ill. Mr. Mitchell conducted the final 16 concerts of that season.

The orchestra's first overseas tour, in 1959, lasting 12 weeks and involving 68 concerts in 19 countries of Central and South America, was taken under his direction. He also directed the orchestra's first European tour in 1967.

As music director, Mr. Mitchell was noted for his interest in American music and in educational programs. Among the notable recordings made under his baton were the first recordings of several symphonies by Paul Creston. He also directed two series of educational recordings for RCA Victor, "The Instruments of the Orchestra" and "Adventures in Music," which are still used in some school systems, though they are collector's items, long out of circulation.

During the orchestra's first 24 years, which included the first half-dozen years of Mr. Mitchell's tenure, each program was usually given only once. He began changing this situation in his first season, with repeats of some programs involving stellar names. By the mid-1950s, all the orchestra's programs were offered at least twice and some more often.

In 1969, Mr. Mitchell was given the title of music director emeritus and was succeeded by Antal Dorati, but he continued to guest conduct regularly. His final concert with the orchestra was in April 1981, its 50th anniversary season. By that time, he was in failing health; the April concert had been postponed from December 1980, because he was hospitalized for surgery.

Mr. Mitchell's wife, Alma, whom he married in 1931, died in 1975.

Survivors include five children and 22 grandchildren.