The House yesterday approved a two-year authorization bill for the State Department that includes a controversial provision to promote democracy abroad under the auspices of a new National Endowment for Democracy.

Opponents of the plan, which would give the endowment $31.3 million a year to dispense to "private sector" grantees, charged that it would turn out to be "at best a boondoggle" and at the same time make its recipients seem like tools of the federal government.

The House, however, on a 215-to-194 vote, decided to inaugurate the program. Foreign Affairs Committee Chairman Clement J. Zablocki (D-Wis.) maintained that a vote against the plan would amount to "supporting totalitarian, undemocratic" regimes.

Critics, led by Rep. Hank Brown (R-Colo.), succeeded in killing proposed $5 million a year allocations by the endowment to organs of the Democratic and Republican parties, but failed in other efforts to unravel the program.

The House then adopted the authorization bill by voice vote. It contains $3.3 billion for fiscal 1984, which will begin Oct. 1, and $3.6 billion for fiscal 1985 for the State Department, the U.S. Information Agency, the Board for International Broadcasting and the Inter-American Foundation, in addition to the non-profit endowment.

Rep. Dante Fascell (D-Fla.), who will become interim chairman of the endowment, defended it vigorously as floor manager of the legislation and cited President Reagan's endorsement of the idea last year in a speech to the British parliament.

The bill allots $31.3 million a year to the endowment "to promote . . . democratic training programs and institution-building abroad . . . to strengthen democratic electoral processes" and finance other such projects "consistent with the broad concerns of U.S. national interests."

In turn, the endowment automatically would dispense $13.8 million a year to the AFL-CIO's long-established Free Trade Institute and $2.5 million to a counterpart to be set up by the U.S. Chamber of Commerce.

Elimination of the $5 million apiece for the just-incorporated National Democratic and National Republican Institutes for International Affairs leaves the endowment with all of the remainder--$15 million a year--to dispense on its own.

Fascell said there would be "sufficient oversight" in both houses of Congress to prevent some of the mishaps and misspending that opponents envisioned. The endowment's records, however, apparently would be exempt from public scrutiny. The bill states that it "will not be an agency" of the U.S. government and thus not subject to the Freedom of Information Act.

Rep. George W. Crockett Jr. (D-Mich.) protested that the project "seems at best a boondoggle," and complained about the makeup of the endowment's proposed "self-perpetuating" 15-member board. Noting that it contains only two blacks, no Hispanics and three women, Crockett said:

"I would question whether this board can sell democracy to the rest of the world when it does not even come close to a cross-section of this country."

While Colorado's Brown failed in his motion to kill the program, he succeeded by 267 to 136 in eliminating the earmarking of funds for the two political party institutes.

The measure includes a two-year total of $217.2 million for the Board of International Broadcasting; $10 million to combat piracy in the Gulf of Thailand, and a three-year total of $28.2 million (starting with fiscal 1983) for "Radio Marti" broadcasting to Cuba, contingent on passage of a separate bill to establish Radio Marti.