Visa Inc's and MasterCard Inc's shares dropped sharply on Tuesday, as Visa's chief executive said a proposed law to curb debit card fees could cut into transaction volumes.

Visa CEO Joe Saunders, speaking at JPMorgan's Technology, Media and Telecom conference, said the latest Senate proposal to curb debit card fees could cause a temporary drop-off in the amount of debit transactions.

Depending on what happens with interchange and the level of interchange, there may be some reduction in the volume in the short run, said Saunders, who cautioned he did not view the legislation as having much long-term risk for the largest U.S. debit processor.

Visa shares fell 7.3 percent to $69.25 in late New York Stock Exchange trading, and MasterCard shares dropped 6.0 percent to $198.07, outpacing the S&P 500 Index's midday decline of 1.3 percent.

Visa and MasterCard receive fees every time a purchase is made on their networks.

Last Thursday, U.S. Senator Richard Durbin, an Illinois Democrat, proposed an amendment to the wider financial regulation bill that would curb debit card fees and allow merchants to cap debit- and credit-card transaction amounts.

Visa shares have declined 18 percent since the amendment's announcement, while MasterCard shares are down 13.6 percent.

The amendment caught all investors by surprise, said Andrew Jeffrey, an analyst with SunTrust Robinson Humphrey, who called much of the share drop overblown. I think we're all just beginning to digest the implications.

Some investors agree that the concerns are inflated. Retailers want to make it as easy as possible for customers to buy, and so are unlikely to put limits on their customers' use of plastic, said Tucker Brown, a research analyst at Sustainable Growth Advisers in Stamford, Connecticut, which owns Visa shares.

Long-term, credit and debt card processors are attractive businesses because they have high earnings growth, strong cash flow, and the potential to benefit as increasingly high percentages of consumer spending involve card use.

They have a very compelling business model, Brown said.

(Reporting by Joe Rauch, editing by Maureen Bavdek and Gerald E. McCormick)