Senate Majority Leader Robert C. Byrd (D-W. Va.) said yesterday that U.N. Ambassador Andrew Young's remark on American political prisoners were of "sufficient gravity that resignation should have been considered" and that if Young makes another "irresponsible" statement he should be fired.

Last week, while two leading dissidents were on trial in the Soviet Union and the United States was condemning Soviet treatment of them, Young told a French newspaper that there are "hundreds, maybe even thousands of political prisoners" in U.S. jails.

Speaking yesterday on the television program "Face the Nation" (CBS, WDVM), Byrd said Young's remark was the "most serioux of a series of irresponsible and rash statements" and that it undercut Carter administration efforts to win better Soviet treatment of dissidents. The remark gave "succor and comfort" to the Soviet Union, Byrd said.

He said he told President Carter and Young that he was "disturbed" by the statement and that "it was a matter of serious concern to me and my colleagues."

"He's made several irresponsible statements, and I think that this last one was of sufficient gravity that resignation should have been considered," the senator said. "And if he makes another irresponsible statement that fits into this pattern of bad judgment, I think he should go."

Young later said he meant that there are "political prisoners" in U.S. jails, but said that ther term "political prisoner" could be defined in different ways.

He said he had never "equated the status of political freedom in the U.S. with that in the Soviet Union. I know of no instance in the U.S. where persons have recieved penalties for monitoring our government's position on civil or human rights."

President Carter telephoned Young Saturday morning and chastized him for his remark. "Andy agreed that it was a mistake, and an unfortunate one, and he apologized for the problems he caused," White House press secretary Jody Powell said.

Byrd, who recently visited Europe as Carter's personal emissary, said NATO allies are "confused, puzzled and alarmed" because of the "many voices on foreign policy."

He also said the Seante will debate repeal of the Turkish arms embargo next week. He siad the "votes are potentially there to stop the embargo," because it has been weakening NATO's southern flank.

He also said he hopes the Senate finishes its work on the energy package, a tax-cut bill, Civil Service reform and a welfare measure. He said he favors a "moderate" $15 billion tax cut beginning in 1979 a reduction in the capital gains tax from 49 to 35 percent.