President Reagan's drive for confirmation of Supreme Court nominee Robert H. Bork ran into new trouble yesterday as Senate Armed Services Committee Chairman Sam Nunn (D-Ga.) vowed to help block action on Bork until Republican senators allow passage of defense and arms control legislation for next year.

The threat from Nunn, influential among moderates whose support is considered essential for Bork to be confirmed, came as the Democratic-controlled Congress returned from a month-long recess to face a heavy agenda complicated by disputes with the White House on most major issues. Nunn did not say how he would try to block the nomination.

Hoping to get off to a fast start, the Senate ended months of delaying tactics by conservatives and confirmed the nomination of Melissa F. Wells as ambassador to Mozambique and prepared for a new test today over legislation to curb the costs of congressional campaigns. It also moved to patch up one of its many quarrels by unanimously approving a bipartisan condemnation of negative campaign tactics, inspired in part by an earlier GOP characterization of Sen. Howard M. Metzenbaum (D-Ohio) as a supporter of "communist causes." In addition, there were preliminary moves in both chambers to grapple with the fiscal crises that Congress faces before the start of fiscal 1988 on Oct. 1.

But, in a sign of controversies that lie ahead, Sen. Jesse Helms (R-N.C.) introduced an amendment to the campaign finance bill that would allocate $310 million in military aid to the Nicaraguan contras unless Reagan certifies that his conditions for a Central American peace plan have been met. The proposal could come up for a vote today if, as expected, a move to shut off a GOP filibuster against the campaign bill fails.

Nunn's warning on Bork was his second move in as many weeks to complicate prospects for key items on Reagan's legislative agenda unless the administration backs down from its insistence on a broad interpretation of the 1972 Antiballistic Missile (ABM) Treaty aimed at permitting expanded testing of the administration's space-based antimissile defense program.

Last week Nunn said he would demand congressional review of the record of current negotiations on a treaty to ban small- and medium-range nuclear forces (INF) in light of the administration's reliance on the negotiating record for the ABM treaty to buttress its case for a broad interpretation of the pact.

His latest threat to help hold up consideration of Bork was made because Republicans, with White House backing, are holding up the fiscal 1988 defense bill because it contains language requiring congressional approval for any reinterpretation of the ABM treaty.

"I can't see bringing up Bork before a defense bill that's been pending for three months," Nunn told reporters. "Until they let the DOD {Department of Defense} bill come up . . . he {Bork} can cool his heels," Nunn added.

"They {the administration} have gotten themselves in a deep, dark hole on the ABM issue," he said.

Nunn described himself as "totally neutral" on Bork's nomination and said his tactics are aimed at forcing a vote on the defense bill. While stopping short of saying he would support a Democratic filibuster against Bork, his position could be significant in early maneuvering over the nomination and in Democratic efforts to end GOP delaying tactics over other issues.

Senate Majority Leader Robert C. Byrd (D-W.Va.) also has warned that Republicans are jeopardizing prompt action on Bork by their stalling tactics, and he called again yesterday for cooperation while warning that Democrats will be wary of "cosmetic bipartisanship."

He said early tests will be made on Central America and fiscal policy and warned the administration that a threatened presidential veto of trade legislation would be a "clear sign to Congress that all bets are off with regard to bipartisanship."

The Wells nomination was confirmed 64 to 24 after the Senate invoked cloture to cut off a filibuster by Helms, ranking Republican on the Foreign Relations Committee, who was holding up action to force the State Department to deal with the Mozambique National Resistance and its insurgency against the Marxist government of the war-torn African nation.

Meanwhile, Republicans proposed their own version of campaign finance reform, which would tighten limits on contributions from political action committees (PACs), strengthen disclosure requirements and curtail other practices that have led to abuses, while stopping short of Democratic proposals for providing public funding for candidates who accept spending limits.

In another development, House and Senate leaders sought again to try to repair the Gramm-Rudman-Hollings balanced-budget law amid conflicting predictions of whether a bipartisan agreement can be reached before the federal debt limit must be extended Sept. 30.

Before the recess, House and Senate negotiators were close to agreeing to revive the budget law's mechanism that forced automatic, across-the-board spending cuts if the White House and Congress fail to agree on steps to reduce the federal deficit. The agreement would likely be attached to an extension of the debt ceiling.

Unless legislators repair the Gramm-Rudman-Hollings law, whose spending cut provision was struck down by the Supreme Court, it is unlikely Congress will make much progress in reducing the federal deficit this year.

To pressure the negotiators, who are also seeking to make the law's annual deficit targets easier to reach, House and Senate leaders will begin today a "fallback" spending cut procedure called for in Gramm-Rudman-Hollings. It would require spending cuts of $45 billion to meet the fiscal 1988 deficit-reduction target of $108 billion.

Congress has sidestepped the procedure in the past. It calls for a joint committee to report a budget-cutting resolution within five days of the end of the recess. It would require spending cuts of $45 billion, including a 13 percent trim in defense programs and a 19 percent reduction in nondefense programs.

Byrd said the fallback is being used to pressure House and Senate negotiators and there is little likelihood Congress will vote on the resolution.