Despite recent reports of political turmoil between President Carter and Congress, Senate Majority Leader Robert C. Byrd (D-W. Va.) praised the president yesterday for "good leadership" on "tough" issues.

Major victories on longstanding issues have been won by Carter in the Senate," Byrd said at his regular Saturday press conference. On Friday House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said he had been "deeply hurt" by the President.

Carter approved the dismissal of O'Neill's longtime friend, Robert T. Griffin, as deputy director of the General Services Administration last week without notifying him, O'Neill complained.

Carter also has had trouble with the No. 2 man in the Senate, Democratic Whip Alan Cranston (Calif.) Carter called him to the White House recently to complain that he had not supported the president on Civil Service reform, the Turkish arms embargo and other measures.

And Sen. Edward M. Kennedy (D-Mass.) joined the fray Friday when the accused Carter of "failure of leadership" on the national health insurance issue. O'Neill, Cranston and Kennedy have been among Carter's strongest supporters in Congress.

Bryd listed some of Carter's recent successes to back up his praise: the Panama Canal treaties, the Middle East arms package and the Senate's vote to the Turkish arms embargo. (The embargo repeal has been gaining support in the House, sources there have indicated.)

These Carter victories "indicate good leadership," Byrd said.