Junior Finance Minister Simon Harris has warned banks to "cop on", or face losing hundreds of customers looking for better rates.
He was speaking after AIB this week reduced its standard variable rate by a quarter of one percent to 3.9%. Bank Of Ireland and Ulster Bank said they had no plans to do likewise.
"Banks need to realise if they don't cop on, and if they try to extort their customers, their customers are going to get up and go somewhere else," Mr Harris said.
"That's not an option for every standard variable rate customer. It is an option for about 150,000 of them though and the Government needs to help convey that message very clearly.
"The Government needs to foster competition (and to) present, through the Central Bank, honest data of what exactly the gap is, and we need to start seeing phased reductions. We saw it in AIB this week and we want to see it in the other banks."
Meanwhile, new measures to specifically target people in long-term mortgage arrears are to be introduced in the next few weeks, with details of the plans to be finalised soon.
Finance Minister Michael Noonan will meet with the four main mortgage lenders next month to discuss the issue.