American Express Co. has cut a deal with Salem Five Cents Savings Bank in Massachusetts to give the bank’s customers free access to Amex’s 320 automated teller machines in the state.

American Express has been building a national automated teller machine network, arguing that banks do not let its cardholders use their machines and that it needs to give these cardholders ready access to cash. The Amex machines are available to bank card holders, but the surcharge ranges from $1 to $1.75.

Most American Express machines were bought last year from Electronic Data Systems Corp. of Plano, Tex., which already had no-surcharge deals with several banks, according to Joanne Fischer, a spokeswoman for American Express.

“This is simply something we inherited,” Ms. Fischer said, “and they were a good partner, so we decided to continue it.” The deal is not part of a larger strategy to pursue relationships with banks through ATM contracts, she said.

The American Express ATMs dispense cash and show account balances but do not take deposits, Ms. Fischer said. “We are not pursuing deposits on these machines at this time,” she said. “But it’s something we’re still evaluating for our network overall.”

Salem Five, which has about a dozen branches in the Boston area, has been trying to augment the number of surcharge-free machines its customers can use. It belongs to the SUM surcharge-free network, a coalition of New England community banks that voluntarily waive surcharges for use of their ATMs by one another’s customers.

Salem Five was also a pioneer in Internet banking, and its separately branded Internet bank, directbanking.com, has drawn customers from around the country. The agreement with American Express applies to both Salem Five and directbanking.com customers.

Directbanking.com customers still must make deposits by mailing them to Salem Five or arranging for direct deposits or wire transfers, said Marie O’Neill, a spokeswoman for Salem Five.

The deal with American Express “does a nice job of extending and creating easy access and convenience for our customers,” Ms. O’Neill said.

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