Federal Reserve Board chairman G. William Miller said yesterday his default by New York City would wreak havoc with the nation's banking system, and is prepared to supply whatever funds are needed to bolster any bank that would be hurt by such a move.

In testimony before the Senate Banking Committee, Miller said the danger to the banking system has abated because most of the banks that held large amounts of New York-related securities during a 1975 crunch have disposed of them since.

As a result, Miller said, while there would be "some effect" on the banking system from a default by the city at this time, "we certainly don't see any series of crises," and the Fed will be able to maintain sufficient liquidity to prevent banks from collapsing.

Miller's comments marked the first major assurances the Fed has given the financial community in the face of a possible default by the city this time. There has been considerable concern in some quarters about the impact of any failure by the city.

Miller's remarks came as, separately, negotiators for the city and its major municipal unions reached agreement on a compromise involving extension of the Emergency Financial Control Board - breaking an impasse on key legislation that was blocking any labor settlement.

The proposal, worked out in Albany after 16 hours of negotiations would extend the board's life as fiscal watch-dog agency for the city, but limit its power to veto labor arbitration awards by giving municipal unions the right to appeal the board's rulings in court.

The agreement was expected to clear the way for prompt action by the New York State legislature to approve the overall legislation and also to enact a companion measure that would increase the borrowing authority of the Municipal Assistance Corp.

Failur of the negotiators to reach agreement before now was a major factor in a decision by Sen. William Proxmire (D-Wis.), chairman of the Banking Committee, to cancel a hearing Wednesday on legislation to provide $2 billion in new loan guarantees for the city.

At the same time, the impasse also had blocked settlement of new two-year contracts for some 200,000 municipal employes. Immediately after yesterday's compromise, Barry Feinstein, one of the union negotiators, predicted contract talks would resume early next week.

The current round of federal aid to New York City expries on June 30. With Congress in recess next week for the Memorial Day holiday, it now seems likely that the earliest lawmakers could renew the loan legislation would be just in time for the deadline. Hearings are expected to resume in mid-June.

Yesterday, the Housr Rules Committee cleared the way for House consideration of the loan legislation by agreeing on a voice vote to send the measure to the floor. House Banking Committee chairman Henry S. Reuss (D.Wis.) urged prompt passage, waring a default could have "serious" effects.