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|Visa users took to social media to complain of problems processing transactions in Europe (AFP Photo/ALAIN JOCARD)|
The blockage had left some customers stuck at the tills in stores across the continent and queueing at cash machines.
"Visa cardholders can now use their Visa cards as we are currently operating at close to normal levels," the company said in a statement.
"The issue was the result of a hardware failure. We have no reason to believe this was associated with any unauthorised access or malicious event."
A spokesman told AFP earlier it was not possible to say how many Visa users across Europe had been affected.
Visa users took to social media to complain and banks tried to explain the situation their customers.
HSBC bank's UK Twitter account earlier said: "From what we understand there are still intermittent issues but services are slowly recovering."
Paymentsense, which provides card machines, online payment gateways and virtual terminals to some 60,000 independent businesses in Britain and Ireland, advised users to try paying via contactless transactions.
"We have been informed that Visa has corrected the outage and transactions are now starting to go through. There is still some intermittency however, we believe this is due to a backlog of transactions," it said.
"We now understand that contactless transactions have a better chance of going through."
It is understood the Bank of England is aware of the issue and is in touch with Visa.
The Royal Bank of Scotland's Twitter help account said cash machine withdrawals were unaffected.
"This is an industry wide issue which is being investigated as a matter of urgency and we apologise for any inconvenience. ATM and MasterCard transactions are not impacted," it said.
In a Primark store on Berlin's Alexanderplatz, frustrated customers were queueing for 20 minutes to pay. Staff did not know why transactions were not going through.
However, in the neighbouring store, transactions were being processed without any problems.
Sandra Foy, who owns a bookshop in Manchester, northwest England, told Sky News television: "I run a small business and the loss of any business is a big deal for us.
"Not knowing when this is going to be sorted out is incredibly frustrating."
The BBC posted a picture of a London supermarket worker standing outside holding a sign reading: "cash only".
It cited Elle Gibbs-Murray, from Bridgend in south Wales, as saying she was stuck in traffic on the Severn Bridge between England and Wales for 45 minutes as drivers were unable to pay the toll by card.
Alex Neill, Which? consumer magazine's managing director of home products and services, said: "Clearly this issue will be a huge inconvenience to customers and it must be resolved urgently. Visa and the banks need to ensure no-one is left out of pocket due to this outage.
"We strongly advise people to keep any evidence of extra expenses they've incurred in order to claim them back."