Secretary of State Alexander M. Haig Jr. said yesterday that the Soviet Union is shipping arms to Cuba in near-record quantities, and that Moscow has given "unsatisfactory" replies to U.S. objections.

Haig volunteered his concern about the Cuban shipments in a closed-door session of the Senate Armed Services Committee while justifying U.S. arm sales abroad and the need for congressional approval of increased funds to facilitate them. The text of Haig's prepared remarks was made public by the State Department.

According to Haig, "Soviet military deliveries" to Cuba in the first seven months of this year were more than twice the volume received during all of 1980. Haig suggested that "with moderate additons" the final total for this year will be the largest since 1962, the year of the Cuban missile crisis.

Haig did not give figures in his published testimony, but told The Boston Globe in an interview that 40,000 tons of "sophisticated" Soviet weapons had been shipped to Cuba so far this year.

Haig told reporters on Capitol Hill that most of the new weaponry is believed to be earmarked for modernization of Cuba's regular armed forces of for arming the new "territorial militia" that President Fidel Castro is forming with the expressed purpose of defending against a U.S. invasion. The militia was originally announced last year but was not actually organized until the Reagan administration came to power in January.

Haig said there is "solid evidence" that some of the Soviet weaponry had made its way from Cuba to Nicaragua and the insurgent forces in El Salvador.

According to Haig, U.S. discussions with the Soviets on the matter, while unsatisfactory to date, have not been terminated.

Using a phrase that has been used to suggest military pressure or force, Haig added, "There are other aspects of going to the source which are under consideration now in respect to the Cuban situation, and those reviews will continue. And that's all I feel it prudent to mention today."

Haig cited the Soviet shipments to Cuba as a "dramatic illustration" of increasing Soviet activity in the developing world which justifies greater U.S. efforts. Haig told the committee that the Soviet Union last year spent $16 billion for arms to the developing world while the United States transferred $10 billion to such countries.

Haig appealed for congressional action on the security assistance program, which is part of the foreign assistance bill, saying that its status in Congress is "alarming." House Democratic leaders have refused to schedule the aid bill until they are assured of necessary Republican votes to put it through.

The aid program has operated without passage of a full-scale bill for the past two years, a "shortsighted approach" which could have "serious consequences" if repeated this year, according to Haig.

In a related development, Pentagon sources said Cuban MIG21 fighters were twice turned back by U.S. Navy F14s southeast of Florida this month when it appeared that the Cubans might be headed for the U.S. aircraft carrier Independence. The sources said the interceptions were over international waters and the planes got no closer than 60 miles from the carrier.