Women and minorities occupy nearly 31 percent of the board seats of Fortune 500 companies, a small increase over the last four years, a new study has found.

While that is the highest level in the six years of the study, white men continue to hold more than two-thirds of the positions.

The data for 2016 — from the Alliance for Board Diversity, an association of groups promoting inclusion of women and minorities in boardrooms, and Deloitte, a professional services firm — underscores that companies have made only incremental progress in promoting diversity in boardrooms.

Corporate boardrooms with directors of varied backgrounds are still relatively unusual. Starbucks, the Seattle-based coffee behemoth, drew public notice last month when it announced that it would add three minority directors. If approved by shareholders, the expanded 14-person board will be 29 percent women and 36 percent minorities.

Those percentages are seldom matched by other large companies, according to the new study, “Missing Pieces Report: The 2016 Board Diversity Census of Women and Minorities on Fortune 500 Boards.”

“With the current rate of progress, we aren’t likely to see the number of minorities and women increase to our target of 40 percent representation until the year 2026,” said Ronald C. Parker, the chairman of the Alliance for Board Diversity. “This is not acceptable. Corporations need to do more to keep pace with the country’s changing demographics.”

Many companies, however, continue to turn to people who have had chief executive experience, and these tend to be men. In addition, only a small number of board seats turn over in any given year — about 350 around the country — which makes it difficult to quickly increase the numbers of women and minorities. The total number of Fortune 500 board seats last year was 5,440, down slightly from 5,463 in 2010.

Most boards range from nine to 11 people — which some companies argue is a reason for the lack of board directors with more diverse skills than those conventionally accepted for board candidates. The relatively low turnover — the average tenure is eight to 10 years — and the small number of companies that have term limits also make the move to broader inclusion less rapid than advocates would like.

A possible bright spot for increasing diversity is that many board members are in their 70s, meaning they are likely to step down in the coming years.

African-American men increased their presence in Fortune 500 boardrooms by 2 percent. Their female counterparts increased their portion of seats by 18.4 percent. But the report also found that African-Americans had the highest rate of serving on multiple boards.

This indicates, Mr. Parker said, “that companies are going to the same individuals rather than expanding the pool of African-American candidates for board membership.”

Hispanic men made a small gain of eight board seats, for a total of 188 seats, or 3.5 percent of the total — compared with the 17 percent they represent in the United States population. Asians, including Asian-Americans, or Pacific Islanders occupied 167 seats, or 3.1 percent of the total.

The numbers at Fortune 100 companies are higher in terms of diversity, Mr. Parker noted, with 35.9 percent of women and minorities, outpacing the nearly 31 percent for Fortune 500 companies. Even so, the gains for women and minorities have been meager since the Alliance began collecting data for Fortune 100 companies in 2004. Thirteen years ago, the diversity figure was 28.8 percent. The study verified each company’s total number of directors and board composition against Securities and Exchange Commission annual filings.

The report mentioned several companies as being among the most diverse, including Prudential Financial, PepsiCo, Aramark and Nordstrom. Those companies had at least one female director and a director who was African-American, Asian, Hispanic or Latino.

More women are being recruited with technology skills as companies adjust to the current economy, said Deborah DeHaas, the chief inclusion officer at Deloitte, who worked on the report.

Even so, women and minorities claimed few of the most powerful board seats, which include leading committees on corporate audit, compensation or governance, Ms. DeHaas said.