The forint traded 0.1% lower, recovering from an earlier fall of around 0.2%. The Czech crown, which like the forint has benefited so far from central bank rate tightening, was down 0.13% in early trade
Polish bond yields were unmoved as markets were looking forward to the central bank's schedule of June bond purchases, due later in the day.
Currencies kept hovering near strong levels they recently hit on rate hike expectations that were fuelled by higher-than-expected CPI data and signals from central banks.
Budapest's BUX index climbed 1.5% on a more than 3% rise in MOL's shares after an update on refinery and petrochemical margins enticed investors.
In Prague, the PX index nudged higher and held above the 1,100 level to stick around highs last seen before the COVID-19 pandemic struck markets in February 2020.
The Polish zloty was 0.54% firmer against the euro at 4.5516, the Czech crown had strengthened 0.09% to 25.8210, while the Hungarian forint was 0.13% stronger at 358.70.
"Over the next few days, the yields of 2-year bonds should remain around 0.05%, while the yields of 10-year bonds should remain close to 1.60%," PKO BP analysts said in a note.
"We think that the (bank's) view has remained relatively unchanged and that it will continue to look for an opportunity to start normalising its monetary policy," Morgan Stanley said.
"We maintain our view that the MPC will start seeing higher chances of a rate hike only in 3Q21."