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Barclays' card-reader system, known as Pinsentry, is used by about 250,000 customers, but it could ultimately be extended to all 11 million current account holders, the bank said last week.
Customers who want to set up a new third-party payment will get a screen warning them that they will have to upgrade to Pinsentry.
Barclays' electronic banking director, Sean Gilchrist, said the move was aimed at cutting fraud "significantly".
Figures released in October by UK payments association Apacs showed that industry losses from online banking fraud were down 67% to £7.5m, but that card-based frauds where the cardholder was not present were up 44% at £137m.
Gilchrist said the extension of Pinsentry to address cardholder-not-present fraud was the logical next step, but Barclays had no firm plans to do so at present.
RBS/NatWest said this week it plans to issue 1.4 million readers to its online retail banking customers by the end of the year.
The bank has sent out hundreds of thousands of card readers since May to businesses and personal customers, but now plans to send them to any customer who sets up a new payee mandate.
HSBC said it had decided against rolling out card readers to its online customers because of the complexity of using them. Only its small-business customers get them if they specifically request them.
"The process that you go through to get online and shop online using one of these takes quite some time and is complex. We tested this with customers, but the feedback was not good," said an HSBC spokesman.
The bank is trialling another form of authentication, which it calls out-of-band authentication, where it will call customers and ask them to confirm a personal identification number.
A spokesman at Apacs said that any form of fraud prevention was good news, but the choice of systems varied because of the different fraud profiles of high street banks. "The banks that are not issuing these may not be experiencing as much fraud," he said.