President Carter pledged yesterday to help solve the problems of small businesses, a group which complains it is bearing the brunt of Carter's anti-inflation policies.

Carter made the promise during a White House Rose Garden ceremony when he received the final support of the White House Conference on Small Business, which met in January.

"There is no doubt in my mind that the small business conference, and the way it was handled, has been one of the major forces in strengthening the American economy and our free enterprise system," Carter said.

"This report will be a milestone, and . . . at the end of this assessment period -- when we are working together, not only with those assembled here but with the Congress and the other members of the business and labor community in our country -- we will come back in 1982 with a good assessment of dynamism and progress."

A follow-up conference is scheduled for 1982, and Carter said he plans to be there, "hopefully not as a small businessman, but who knows? That is a judgment for the American people to make."

A press conference following the ceremony was held by conference chairman Arthur Levitt Jr., chief executive of the American Stock Exchange, and A. Vernon Weaver, head of the Small Business Administration, who both defended Carter's record on small business.

"The importance of the Rose Garden ceremony was that it occurred," Levitt said. "Small business could become a most important economic lobby."

But Levitt and Weaver were asked why small businesses were failing rapidly as a result of Carter's anti-inflation drive if they were considered to be so important.

"I'm not implying these aren't difficult economic times," Weaver replied. "I'm saying this sour medicine" that the nation must swallow was designed by Carter "to put the least impact on small business."

A recent SBA report said that because of the administration's anti-inflation policies small business bankruptcies have increased 48 percent and about 266,000 more small businesses, in addition to the 400,000 that on average fail each year, are expected to go under.

Weaver said that many bankers didn't understand that the administration's inflation-fighting policies encourage banks to continue making loans to small businesses.

The report to Carter presents the 60 recommendations of small business delegates to the convention in January, many on capital formation and tax-cut proposals.

Some of the commission's proposals include establishing:

A more graduated corporate income tax to reduce taxes at the low end of the rate schedule by pushing the top rung of the tax-rate stepladder from $100,000 in income to at least $500,000 and comparable relief for sole proprietorships and the self-employed.

Tax credits for direct-equity investment in new small business corporations.