WASHINGTON — Sen. William S. Cohen charged Tuesday that thousands of needy Maine residents have been denied Social Security benefits they may be entitled to because of bureaucratic mistakes.

During a Senate hearing it was reported that a nationwide study recently concluded that 65 percent of persons eligible for benefits under the Supplemental Security Income program were denied benefits.

Although there was no estimate for the number of persons unfairly denied SSI benefits in Maine, Cohen said that 23,100 residents of the state currently are enrolled in the program. The new study, he said, suggests that “there are many thousands in Maine who could be on the SSI rolls if they applied.

SSI sends monthly checks to people who are at least 65, or blind, or disabled, who have limited income and resources.

The Maine senator said that Pine Tree Legal Service Corp. lawyers in Maine indicated that the Social Security Administration’s nationwide 800 number actually may be discouraging applicants from appealing their rejections by SSI officials.

That criticism was echoed during a House hearing on problems with the Social Security system.

According to a new General Accounting Office report, the administration’s new telephone system is leaving many people waiting in vain for their calls to be returned, government auditors said Tuesday.

GAO said that, in some types of cases, 42 percent of callers never received the follow-up calls they were promised when they dialed Social Security’s toll-free 800 number.