Sen. William Proxmire (D-Wis.), chairman of the Senate Banking Committee, yesterday backed off his stance that he would not hold hearings on aiding New York City until the city and its labor unions came to terms on a three-year settlement.

Proxmire announced yesterday that he would hold four days of hearings on proposed New York City financial aid legislation starting June 6.

The House Banking Committee has approved a bill that would provide federal guarantees for up to $2 billion of long-term New York City securities starting July 1. The federal government's current seasonal assistance expires June 30.

The House bill is esentially the one proposed by the Cater administration last March. The assistnace would be provided through June 30, 1982, at which time New York City is supposed to have its budget in acutal balance and be able to borrow on its own in the capital markets, something it has not been able to do since 1975.

A key to the city's ability to balance its budget is the outcome of labor negotiations that have been in progress for three months. The current contract with its municipal employes expires June 30.

Proxmire, in announcing the hearings, said it has "become abvious that the committee will have to go ahead with hearings in order to give timely consideration to the New York City aid proposals pending before us."

But Proxmire warned it will be "difficult" for the committee to make "an informed decision on this important legislation in the absence of a resolution (of the labor situation)."

Proxmire said that "failure to resolve these matters by the date of the hearings will certainly add to the problems the city already faces in presenting its case for further iad to New York City."

The city and the unions had pledged to reach an agreement by May 20 and Proxmire tentatively scheduled hearings and the municipal unions missed the May 20 deadline.

Both parties have reported progress in the negotiations. Mayor Edward Koch has said that the cannot afford to give unions an agreement that will cost the city more than $610 million.

The unions have said they want a settlement as least as good as the one reached with the transportation workers, who received a pact that would cost the city between $800 and $900 million if municipal workers received the same package. The state picked up most of the tab for the transport workers - who have yet to ratify the agreement.