The involuntry merger of Greenwich Savings Bank in New York City into New York's Metropolitan Savings Bank, which was announced late Wednesday night by the Federal Deposit Insurance Corp., is the fourth mutual savings bank merger in New York State in the past year. And it probably won't be the last.

Analysts say that two other banks, New York Bank for Savings and Union Dime Savings Bank, are in "desperate need" of finding merger partners within a year before their losses entirely erode their capital. Other savings banks in that state have reserves that would permit them to sustain losses for up to five years.

Only three out of 38 state-chartered mutual savings banks in New York had profits during the second quarter of this year. Greenwich, with assets of $2.2 billion, had losses of $18 million in that period and $14.4 million in the first quarter. At that rate, its reserves of $61.3 million would have run out in the first half of next year.

Metropolitan, with asets of $2.2 billion, had losses of $5.5 million in the period but held reserves of $131.5 million--which means that it could sustain that size loss for years without running out of capital. The losses occurred because the institutions were paying out more interest on deposits than they were receiving on mortgage loans.

Metropolitan merged in early October with Brooklyn Savings Bank. Together Metropolitan-Greenwich-Brooklyn, which will be known henceforth as Metropolitan, has deposits of about $5.9 billion. That makes it the second-largest savings bank in the country, behind Philadephia Savings Fund Society with deposits of $7 billion.

All 315,000 customers of Greenwich automatically became customers of Metropolitan. All accounts--uninsured over $100,000 as well as those insured up to that amount--will be safeguarded intact.

The merger will cost Metropolitan nothing, but it will cost the FDIC $185 million. Had Greenwich been allowed to fail, it could have cost the government insurer more than $800 million. And it would have caused an immeasurable loss of public confidence in thrift institutions, according to FDIC Chairman William Isaac.

The FDIC put the deal together in a week from proposals submitted by three banks. As part of the terms, the FDIC will repay Greenwich's loan of $340 million from the New York Federal Reserve Bank.