The decision comes after the branches opened for the first time on a Sunday as staff battled to deal with a backlog of payments following last Tuesday's IT glitch.
The banks tweeted: "We're making progress in putting things right and will keep 1,200 branches open until 7pm today and from 8-6pm for the rest of the week."
The debacle rolled into a seventh day after parent company RBS said it was still experiencing technical issues and confirmed some online services were unavailable.
The fiasco, which is also affecting RBS and Ulster Bank, has left many frustrated customers unable to access internet banking.
The three banks have a combined total of 16.9 million account holders.
During the past week, people have seen payments to go awry, holiday and home purchases interrupted and wages appearing to go missing.
NatWest alone has more than 7.5 million personal banking customers, but it remains unclear how many have been affected after the problem made headlines last Thursday.
Susan Allen, of RBS Group, insisted that progress was being made and suggested customers would see their accounts largely "back to normal" at the start of the working week.
"The knock-on effects of this technical failure mean there will be bumps in the road," she said.
"We will do everything we can to minimise further disruption to our customers."
But customers have complained about being without access to cash over the weekend or unable to pay bills.
Karen Eden told Sky News: "It is a worry because you don't know if bills are being paid or not, I'm hoping that they have been but until I get my statement it's going to be difficult to find out."
Customer Abuka Valentine-Iroha added: "I was here on Friday and it was not working, I came back on Saturday and it was the same thing, then to my great surprise it's working now."
Stephen Hester, chief executive of NatWest owner RBS, issued a public apology over the matter and told Sky's City editor Mark Kleinman: "The first thing I must say, and repeat what I said over the weekend - we are very sorry for the inconvenience this has caused our customers.
"Our customers come first for us. We're doing everything we can to put that right."
He added: "I hope as quickly as possible we can put this behind us and learn the lessons and move forward.
"We need to make sure there are no consequences for people's credit ratings."
His comments came amid mounting fears that thousands of people could be hit with penalty charges if their regular payments - including mortgages - were affected.
The computer software problem has been blamed on an attempt to install a software update on RBS's payment processing system, which was then corrupted.
It has promised that any overdraft fees or charges on current accounts incurred by customers would be automatically waived and has said it would work directly with credit agencies to ensure no-one's credit score was affected.