It comes amid news the backlog caused by technical problems, which left thousands of people without access to their accounts, may not be fully resolved until Monday.
Many customers get their salaries on the last day of the month - including hundreds of public sector workers, many of whom are uncertain if money will be in their accounts.
The bank said there should be "no issue" with people accessing their wages if they bring a form of ID and a payslip or other evidence of payment.
However the consumer watchdog said customers are still having difficulties.
"Since this crisis started, the Consumer Council has repeatedly been told by Ulster Bank that customers will have no problems accessing their own money at an Ulster Bank branch," said Antoinette McKeown, Chief Executive of the Consumer Council.
"However, it appears that some customers are having difficulty getting hold of cash at an Ulster Bank branch.
We've heard cases where customers have been set a limit on how much they could withdraw, been refused cash from their savings account, or simply told they couldn't withdraw any cash at all.
"This is completely unacceptable," she added.
Stephen Cruise of Ulster Bank admitted it is "unacceptable" that customers have been left in this position, but said the bank is working to resolve its issues.
"It has been a mighty complex and delicate situation and we are working through the process, hopefully this weekend we will get through it," Mr Cruise told UTV.
"Our anticipated delivery is to get ready by next week. It is unacceptable for customers to be in that position but that is what we are aiming for - the beginning of next week."
On the subject of Direct Debit payments he added: "From 21 to 29 June, any Direct Debit received by the Ulster Bank has been paid."
He also warned customers that the bank does not ask for details to be sent by email.
Ulster Bank said 32 of its branches have extended opening hours until 7pm.
Twenty-six branches will open on Saturday from 10am to 3pm and on Sunday, and 10 branches will be open from 10am to 1pm.
Customers can call also call their helpline over the weekend from 8am-10pm on 0800 231232.
Land & Property services have advised customers who pay their rates monthly by direct debit that if their payment does not go out on Friday they will request a double payment on 31 July.
If customers are unable to manage a double payment they can contact the LPS Direct Debit team by the 19 July on 0300 200 7801.
Northern Ireland politicians have been critical of the bank's treatment of customers.
Roy Beggs of the UUP said: "I have learnt of the desperation of some local Ulster Bank customers in East Antrim who have been unable to visit their bank before going to work. Some have had to take time off work to try to access their money.
"We are now ten days into this crisis and it is absolutely intolerable that local people who are customers of the Ulster Bank still cannot access their funds."
Alliance MLA Stewart Dickson said: "This has been an absolute fiasco. Ulster Bank have serious questions to answer on how poorly they have handled this situation.
"The chaos that has resulted from this problem has knocked the public's confidence in Ulster Bank."
Sinn Féin's Phil Flanagan said: "We are almost a week into this debacle and still key questions remain unanswered.
"How did a relatively minor software upgrade lead to such widespread disruption of the Ulster Bank's payments system? Was there a back-up or recovery system and if so did this also fail? If there was none - why not?"
On Tuesday, the Royal Bank of Scotland Group (RBSG) issued a statement to say that RBS and Natwest customer account balances had cleared overnight - with the exception of a few specific sets of transactions.
Jim Brown from Ulster Bank group said RBS and Natwest accounts were sorted sooner because of their system's "sequencing".
"The priority for the group is to get the customer services to actually get back to normal as quicky as we can for all three but there is a sequencing in terms of how the system's run, the system's design that does impact on our ability to process the transactions and clear up the backlog," he said.
The Bank of England governor Sir Mervyn King said on Tuesday that bank bosses should be subject to a "detailed investigation" over what went wrong and why it has taken so long to sort out the issues.