ANZ has cut home loan and term deposit rates between 10 and 30 basis points (BPS).
The popular one year fixed special mortgage rate is falling 29 basis points to 6.85 percent, and the two year rate by 30bp to 6.49 percent.
Local managing director for personal banking Grant Knuckey said market conditions had changed in recent weeks.
"Following the OCR (official cash rate) announcement last week, we've seen a drop in wholesale rates so we're able to pass on savings to our customers.
"In recent years many people have typically fixed their home loans on shorter terms. That means many will soon be in a position to take advantage of these lower rates."
At the same time ANZ cut term deposit rates by 10 to 30 BPS for 6-month and longer terms because of recent decreases in wholesale rates and the reduction in home loan rates.
Last week Westpac led the sector with cuts to similar levels as ANZ for lending and deposit rates.
A slowing of inflation to an annual rate of 3.3 percent has prompted economists to forecast official cash rate cuts as early as August, but most definitely by November.