Chief Justice Warren E. Burger won "surprising" support from the nation's lawyers for his contention that between one-third and one-half of American attorneys are not competent to represent clients in a trial, according to an American Bar Association poll.

While 51 percent of the lawyers surveyed disagreed with Burger, he was supported by the wealthiest and most influential of the nation's attorneys - those who earn more than $50,000 a year, those who practice in big cities and those who belong to the larger law firms.

On the other hand, small-town lawyers practicing in middle-sized firms (three to 10 attorneys) disagreed most with Burger.

The ABA Journal, which published the poll in its current issue, called the findings "surprising in view of the fuss raised by Burger's statements and the unsuccessful attempt made at the 1978 midyear meeting of the ABA House of Delegates to have him either prove his figures or retract his statements."

In a series of speeches over the past 10 years, the chief justice has attacked the ability of trial lawyers and called for special certificates before an attorney can appear in court.

His remarks were largely ignored by the organized bar until November, when a wire-service report on testimony he had given earlier to a British commission ignited a rare attack by lawyers who may one day have to appear before him.

The attack on Burger was defused at February's ABA meeting, but not before Attorney General Griffin B. Bell cast doubt on the chief justice's estimates and ABA President William B. Spann Jr. said only 20 percent of the nation's lawyers are incompetent to handle trials.

The ABA poll, conducted among 599 lawyers in late March, found that 41 percent agree with Burger. Sixty percent supported his proposal that only lawyers who have special certificates, indicating they have taken extra training in trying cases, be allowed to appear in court.

Lawyers who listed themselves as specialists in trial work gave the proposal its strongest support, with 72 percent of them favoring it.

The lawyers thought that attorneys who want to appear in court should take special training in law school or work as an apprentice immediately after being admitted to practice.

Burger has said his estimates are based on conversations with federal, state and local trial judges across the country.

Yet a nationwide survey of federal judges conducted by the Federal Judicial Center, a pet project of Burger, found that the judges rated only 9 percent of the lawyers appearing before them as inadequate. But 40 percent of the federal judges said they think inadequate legal representation is a "serious problem" in their courts.

"Any problem in the courts which 40 percent of the judges characterize as serious demands our attention, no matter how many or how few of these advocates merit the label of incompetent," Burger told the ABA in February.