ALBANY — When New York State officials agreed to allow local governments to use an unusual borrowing plan to put off a portion of their pension obligations, fiscal watchdogs scoffed at the arrangement, calling it irresponsible and unwise.

And now, their fears are being realized: cities throughout the state, wealthy towns such as Southampton and East Hampton, counties like Nassau and Suffolk, and other public employers like the Westchester Medical Center and the New York Public Library are all managing their rising pension bills by borrowing from the very same $140 billion pension fund to which they owe money.

Across New York, state and local governments are borrowing $750 million this year to finance their contributions to the state pension system, and are likely to borrow at least $1 billion more over the next year. The number of municipalities and public institutions using this new borrowing mechanism to pay off their annual pension bills has tripled in a year.

The eagerness to borrow demonstrates that many major municipalities are struggling to meet their pension obligations, which have risen partly because of generous retirement packages for public employees, and partly because turbulence in the stock market has slowed the pension fund’s growth.