Network Exchange, an automatic-teller-machine network shared by 13 financial institutions in the District, Virginia and Maryland, was activated for public use yesterday, making it the largest operating system of its kind in the region.

More than 140 ATMs in the Network Exchange system are now operational, enabling customers of the 13 institutions to make cash withdrawals and perform balance inquiries at machines of member institutions in all three jurisdictions.

Network Exchange members estimate that, by 1983, more than 250 ATMs will be available to more than 1.5 million Network Exchange cardholders throughout the District, Maryland and coastal Virginia.

The new ATM network is one of four that will be operating in the region by the end of the year. Most banks and savings and loan associations, as well as major credit unions in the region, probably will be tied into one of four networks within a year.

By 1984, more than 1,500 ATMs will be available to customers of more than 50 institutions in four networks extending from the Virginia-North Carolina line to Maryland's borders with Delaware and Pennsylvania.

In fact, spokesmen for two of the region's four ATM networks predict expansion that will include banks and savings and loan associations in the Carolinas, West Virginia, Pennsylvania and Delaware.

Networks of that magnitude would enable an individual holding an ATM card from a District bank, for example, to withdraw cash or perform other banking functions at an ATM of a participating S&L in Raleigh or Philadelphia. Transactions will be switched electronically to be recorded in the customer's bank account.

Money Exchange, the area's first ATM network, has been available for use by customers of the three First American Banks in the District, Virginia and Maryland since July 1980. Money Exchange cardholders have access to 96 ATMs in the District and the two adjacent states.

Three major regional banks announced in April that they plan to license other financial institutions to operate as participants in an ATM network called Cash Flow. The program, which represents an expansion of a system developed by Virginia National Bank of Norfolk, initially will link ATMs operated by Riggs National Bank of the District and Mercantile Bankshares Corp. of Baltimore.

Last week, the largest consortium of financial institutions in the region announced plans to establish a shared ATM network that will link 500 machines electronically by early 1983. Several will come on line in September in the initial phase of the system, which will be called EFT Group.

Spokesmen for EFT Group, which includes American Security Bank and Bank of Virginia, project that member-institutions will have at least 1,000 ATMs on line within two years.