President Carter signed the second veto of his administration yesterday, this time using his ultimate legislative weapon to doom a rabbit meat inspection bill.

In a 400-word, straight-faced veto message to the House, the President suggested that the rabbit bill, among other things , would "strain relations with the People's Repubic of China," a major exporter of domesticated rabbit meat to the United States.

Also, Carter said, the bill was written and passed by Congress for no compelling reason other than to benefit a specialized industry that serves a relatively small number of consumers.

Spokesmen for the nation's $10 million-a-year rabbit meat industry, brushing aside the inevitable jocose commentary on the veto, said there is nothing funny about Carter's actions.

They complained that all the bill would have done would be to elevate rabbit meat to the same safety standards that now apply to goat meat and donkey meat.

Moreover, they said, inexpensive and protein-rich rabbit meat is now on a growth threshhold roughly equivalent to where chicken was at the turn of the century, and the veto will deprive millions of consumers of its benefits.

Carter signed his first veto last week, of a bill to authorize development of an $80 million experimental plutonium-producing breeder reactor at Clinch River, Tenn.

The sponsor of the rabbit bill, Rep. Keith G. Sebelius (R-Kan.) was only slightly crestfallen at the news of the veto when he was reached at his farm at Norton, Kan.

"I'm sorry, of course, but not surprised," he said.

He noted that President Ford vetoed an identical bill last year, an action he suggested is relatively strong for a bill which drew little opposition when hearings were held before the House Agriculture Subcommitee on Livestock and Grains.

Sebelius, who co-sponsored the bill with Sen. Bob Dole (R-Kan.), said he wrote Carter a letter saying that federally funded inspection of rabbit meat would create new jobs for the elderly, handicapped, minority groups and young people, and advantage over rabbit exporters. And "Why let the Red Chinese take over?" he asked yesterday.

Present law does not require that rabbit meat be inspected the way beef and poultry must be before sale for human consumption.

But some large rabbit meat processors participate voluntarily in a Department of Agriculture inspection program. Unlike beef and poultry producers, they must bear the cost of inspection. They do so in the belief that a government inspection stamp will encourage consumption.

Sebelius said his bill, which would have cost the government $52,000 the first year and rise to a maximum of $400,000, would have created and a compulsory, no-fee inspection and grading system similar to that used in beef and poultry processing.

The bill would have applied only to processors of 20,000 or more rabbits a year, thereby not affecting farmers, who breed rabbits as a sideline.

In his veto message, Carter said signing the bill would "provide an incentive for federal payments for the inspection of other exotic and specialty foods," and would also be unnecessary because there has never been a significant health problem with rabbit meat in this country.

Moreover, Carter said "on-site inspection of foreign processing facilities by Department of Agriculture employees would strain relations with the People's Republic of China . . ."

Paul Dubbell, spokesman for the nation's major rabbit meat producers, responded in a telephone interview, "That's a little hard for us to swallow. This was a consumers' piece of legislation, and they're the ones who will suffer."

Dubbell is president of Pel-Freeze, Inc., in Rogers, Ark., which processes 2 million pounds of rabbit meat a year, of an estimated 6 million pounds produced annually in the United States.

Pel-Freeze has 800,000 rabbits in its hutches, and the firm hopes to double that by 1981, a goal Dubbell conceded is within reach, given the rabbit's demonstrated record of proliferation.

Patrick Roberts, Sebelius' legislative assistant, said that rabbits, with a high meat-to-bone ratio and an economical feed-conversion rate of 4 pounds feed to 1 pound weight gain "could put the rabbit where the chicken is in popularity."

In 1909, Roberts said, Americans consumed an average of 14.7 pounds of poultry, and they now consume more than 41 pounds annually.

"The same thing could happen to rabbits, he said, noting that rabbit meat is "well-documented as being low in chloresterol and dieticians swear by its health values . . . We feel consumers have been denied something by this veto.

The House subcommittee has estimated that between 6 and 20 million Americans consume about 2.3 million pounds of rabbit meat each year.

Along with the veto message, the White House issued a stern statement saying, "The President feels that this is a prime example of a bill being drawn up, passed and sent on to the executive branch for no compelling reason - a special interest bill which, is signed, would open the way for more mandatory regulations and increased costs.

Sebelius's staff did not seemed intimidated by the White House message.

"We've been down this trail before, so I have no doubt we'll do it again," Roberts said.

In the meantime, Sebelius said he plans to negotiate with Agriculture in hopes the government will implement some sort of an interim rabbit meat inspection program.