President Carter yesterday overruled his Interior Secretary and recommended that Congress move the nation's mine safety program from the Interior Department to the Labor Department.

It was the first major governmental reorganization proposal Carter has backed since he proposed establishment of a new Department of Energy earlier in the year. That measure also would strip the Interior Department of some programs.

The administration announced support for a bill by Sen. Harrison Williams (D.N.J.) to transfer the Mining Enforcement and Safety Administration (MESA).

Interior Secretary Cecil D. Andrus announced Carter's position in testimony to a Senate Labor subcommittee. Andrus said he favors retaining MESA in Interior but would abide by Carter's decision.

The bill also would strenghen enforcement of mine health and safety laws, impose stricter penalties for violators and combine for the first time programs relating to coal, metal and mineral mines.

Andrus said Carter had decided only on Thursday to back the transfer. "This is encouraging to those of us who have worked on [mine safety issues] for decade . . . it is a magnificent statement," said Williams, chairman of the Senate Labor Commitee.

Williams and other MESA critics have complained that the agency is ineffectual and should not be housed in the Cabinet department also charged with promoting increased coal production.

The Labor Department now oversees other occupational health and safety laws.

A MESA spokesman said the President's decision surprised the agency.

Andrus acknowledged that the current program administered by MESA leaves much to be desired. He said under existing rules it is often cheaper for mine operators to "pay the penalties than to strive for a violation-free mine."

Andrus said the administration supported amendments he claimed would strengthen the proposal. They include an increase of maximum penalties for violators from $10,000 to $15,000, along with a mandatory $1,000-a-day penalty on mines that do not correct safety hazards. Also included is an 8 per cent interest charge against all tardy payments.