The council left the O/N deposit rate, at the bottom of the "interest rate corridor", at 12.5%.
The policymakers had cut the O/N collateralized loan rate by 450 bp at the previous monthly meeting in April.
In a statement released after the meeting, the council said its members had also decided to cut the interest rate on the MNB's one-day quick deposits offered at daily tenders by 100 bp.
The deposits have been offered at a rate of 18% since their launch last October.
The measure was made possible by "the persistent improvement in risk perceptions", the council said.
Policymakers pointed to a "sustained and significant" improvement in domestic financial market stability, driven by both domestic and external factors, as well as "widely improved" investor sentiment towards emerging economies, a "strong and trend-like" improvement in Hungary's current account balance, and stable capital and liquidity positions of domestic banks.
Looking ahead, strengthening monetary policy transmission will be "an important factor" in achieving price stability, the council said, adding that MNB would use instruments to soak up interbank forint liquidity "on a long-term basis" in the coming period.
The council reiterated that maintaining the base rate at its current level "over a prolonged period" was necessary to ensure inflation expectations were anchored and the inflation target was achieved in a sustainable manner. The policymakers said financial market stability was "key" to achieving price stability and that a "cautious and gradual" approach was warranted in the current environment.
"The [MNB] is constantly assessing incoming data and developments in the outlook for inflation and is closely monitoring the effects of international financial market developments on the domestic risk environment. If the improvement in risk perceptions persists, the [MNB] will continue the gradual convergence of the interest rate conditions of one-day tenders to the base rate," the council said.
At a press conference, MNB governor György Matolcsy said the reduction in the one-day quick deposit rate marked the start of the "normalization" of monetary policy while adding that it "could be a long time" before policymakers weighed a cut to the base rate. The central bank will continue its "tight" policy, and bringing down inflation will remain its "primary goal", he added.
Matolcsy acknowledged the government's shift to a path of fiscal consolidation and suggested monetary and fiscal could advance in tandem.
Deputy governor Barnabás Virág said disinflation was expected to accelerate in the coming months, helped by base effects, adding that real interest rates could be positive by year-end.
The minutes of the policy meeting on Tuesday will be released at 2 p.m. on June 7.
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