The Reagan administration yesterday opposed a conservative political drive to make picket-line violence by union members a federal crime.

But the administration did support a proposal to "clarify" a 1973 Supreme Court ruling that critics say exempts union members and leaders from federal prosecution in acts of extortion by violence.

The administration's judicial hairsplitting before the Senate subcommittee on criminal law disappointed some of its conservative backers, led by the National Right to Work Committee, who have spent over $100,000 in a year-long campaign to bring violent picket-line behavior under federal criminal law. The right-to-work group, which opposes what it calls "compulsory unionism," wants to amend the Hobbs Act, the federal anti-extortion and robbery statute, to achieve its objectives.

But the administration's position was mildly pleasing to union leaders with whom President Reagan has been trying to develop better relations. That effort to get on better ground with unions was highlighted by Labor Secretary Raymond J. Donovan's announcement yesterday that the administration has created a labor-government committee designed to "help foster better communications between the administration and organized labor."

Organized labor at first was lukewarm in its opposition to the Hobbs amendment campaign, which earlier appeared to have little chance of success. But the right-to-work committee, largely through a sophisticated mail-order and media advertising effort, began winning substantial public support for its cause--a development that shocked the AFl-CIO and other labor groups into launching an equally sophisticated counterattack.

AFL-CIO and Teamster union leaders who met separately with President Reagan last week told him that the proposed Hobbs Act changes discriminated against employes who may be the targets of employer violence in labor-management disputes, and that the amendments represented an unnecessary federal intrusion into state and local law enforcement.

Robert Bonitati, White House chief of labor liaison, said Reagan told the union leaders that he had no formal policy on the proposed changes, but that he "saw no evidence that these matters picket-line and related violence could not be handled by state and local authorities."

Jonathan C. Rose, assistant U.S. attorney general for legal policy, restated that position in his testimony yesterday. He said placing picket-line and related violence under federal jurisdiction "would . . . create new federal crimes, predicated independently of extortion or robbery. . . ."

"Under these new provisions, the mere assault on a cab driver, who as part of his business occasionally makes interstate trips, or the destruction of his cab would become a federal crime. The federal government could be called on to prosecute such crimes, which are now more appropriately handled by local authorities," Rose said. He said such "an extremely broad expansion of federal criminal enforcement responsibilities . . . is not justified."

But Rose said he believed there was some merit to the right-to-work group's argument that the Supreme Court's 1973 ruling in United States vs. Enmons, in which a group of utility workers were indicted under the Hobbs Act for the "wrongful use of force" in a contract dispute, was drawn too narrowly. The court ruled that the act's prohibition against extortion does not apply to labor-management disputes in which wages and other benefits are at issue.

Rose said the administration's support for a review of that ruling should not produce a new category of federal crimes, but should clarify that "the federal law against extortion would apply to the kind of coercive violence represented by the facts in the Enmons case."