Australia’s banks have come under pressure to reduce borrowing costs for customers after the Reserve Bank cut interest rates to a new historic low of 1.25%.

The widely expected move by the central bank on Tuesday saw its cash rate fall for the first time since August 2016, with many economists predicting there could be two further reductions in borrowing costs before the year ends in the face of a weakening economy.

The RBA’s decision prompted the Commonwealth Bank and NAB to give borrowers a boost by reducing their own standard variable rates by 0.25% points.

But the treasurer, Josh Frydenberg, said he was “deeply disappointed” by the decision by ANZ bank to pass on only part of the rate cut. Its customers will see their standard rate fall by 0.18%, with the bank holding back 0.7%.

Later on Tuesday, Westpac followed ANZ into the treasurer’s bad books by announcing a cut of just 0.2% in its standard variable rate.

Frydenberg told a media conference that ANZ had “let down” its customers in a move that comes despite him earlier warning banks to respond to public expectations by passing on the full benefits of any RBA cut.

“I think the ANZ has let down its customers. This is deeply disappointing from the ANZ. We heard from [banking royal] commissioner Hayne just months ago that the banks were putting profits before people,” he said.

“Actions like this don’t give the Australian people any comfort that the banks have changed their behaviour.”

Small lenders such as Athena, RACQ and Reduce Home Loans increased the pressure on their bigger counterparts by passing the rate cut on in full on Tuesday. Westpac was yet to make its decision.

Sally Tindall of the comparison website RateCity echoed the treasurer’s anger with ANZ.

“ANZ’s decision to not pass on today’s cut in full is a huge disappointment.”

Announcing the rate cut, the RBA governor, Philip Lowe, said it would help speed a reduction in unemployment after the uptick in April to 5.2%, and make more progress towards lifting inflation higher towards the bank’s target of 2-3%.

Lowe said there had been few inroads into the spare capacity in the labour market unemployment but increasing labour force participation, a high vacancy rate, reports of skills shortages and an expected pick-up in wages augured well.

“Taken together, these labour market outcomes suggest that the Australian economy can sustain a lower rate of unemployment,” Lowe said.

The Australian dollar rose against its US counterpart from US69.74c immediately before the decision to as high as US69.93c, before easing back to US69.76c. The ASX200 stock index rose 0.25% on the day.

Lowe was expected to give more clues about the future direction of rates in a speech in Sydney on Tuesday night, but many economists expect more cuts this year.

Capital Economics, which predicted in January that the RBA would be forced to cut this year, said rates could fall to 0.75% by the end of the year.

It noted that Lowe stuck to his “glass-half-full rhetoric” about the Australian economy but Capital thinks analysts are too optimistic about the outlook. It sees GDP falling to 1.5% compared with the bank’s 2.75% forecast and inflation staying at 1.7%.

“The upshot is that we expect the RBA to slash rates to 0.75% before the year is out. Rates falling below 1% will surely heighten speculation that the Bank will soon launch quantitative easing but we think that’s rather unlikely.”

Sally Auld at JP Morgan agreed, saying that the governor’s statement after the meeting was more “dovish” than it sounded. She said rates could fall to 0.55 by this time in 2020.

“We expect the RBA has further to go from here. We are forecasting the next [0.25%] rate cut in August, and a further [0.5%] of easing in [the first half of 2020],” she said in a note.