Congress took the first step yesterday toward keeping New York City solvent after the government's special seasonal loan program to the city expires June 30, but a final aid package is still a long way off.

The House Banking Committee's subcommittee on economic stabiliation approved, on a 12-to-2 vote, a bill which would authorize up to $2 billion in federal loan guarantees to New York City securities over the next four years.

The plan, with minor modifications, is the one developed by the Carter administration last March. The aid plan assumes that New York City will have a truly balance budget by 1982 and will then have the access to the credit markets it does not have today.

The full House Banking Committee will take up the bill next Wednesday and banking chairman Henry S. Reuss (D-Wis.) said he is optimistic that the committee will approve the bill.

At the same time, New York City Mayor Edward Koch yesterday presented a $13.5 billion city budget for the next year as well as an additional $538 million capital budget.

New York City officials said that the city will not be able to borrow enough money to finance its capital budget unless Congress passes the $2 billion loan guarantee program.

The House Banking Committee Chairman William Proxmire (D-Wis.), has said he will not take any action on a New York assistance program until the outcome of negotiations between the city and its municipal employe unions are complete.

Those negotiations have been stalemated for weeks with the municipal unions demanding parity with a settlement agreed to last month by officials of the Transit Workers Union and the New York Transit Authority. The state picked up most of the tab for that settlement, however, and the city maintains that it cannot afford to pay its own workers as much as the transit workers received.