Governor Jiri Rusnok said the bank may act because of faster wage growth and a weaker-than-expected crown.
Regional assets took a hit in May due to advances in the dollar and US rates, and concerns over political uncertainty in Italy and Spain.
"Nerves over both countries have calmed down, the Italian 10-year bond yield is sharply down... there is no bad news," one Budapest-based fixed income trader said.
Hungary's 10-year bonds traded at a yield of 3.03 percent, down 7 basis points from Monday's fixing.
Hungarian bond yields have dropped by about 10 basis points since Italy formed a new government on Friday, with the curve flattening, the trader said.
"People are afraid to sell. Those who bought papers when yields were rising (last month), keep their positions so as to come out with gains," the trader added.
In Romania, where inflation is the highest in the region, bids for bond yields continued to tick up after the central bank cut liquidity in markets via a rare deposit auction on Monday.
Regional markets have largely ignored divergence in monetary policies in the region's main economies during the last weeks' selling and the past days' recovery.
The Czech and Romanian central banks have started to increase interest rates, but Hungary and Poland have signalled no change in their record-low rates for years, and the Polish central bank is expected to reaffirm that stance on Wednesday.
"There will be probably no surprises (when it comes to the central bank), so it should not affect the market as well as the quotation of domestic currency, which should follow the global trend", Citigroup said in a note.
The leu and the forint firmed 0.1 percent against the euro by 0849 GMT, the zloty 0.2 percent and the Czech crown 0.3 percent.
The latter three currencies are off multi-month lows reached last week, and the leu off a one-month low.
Regional stock markets were mixed after the past days' rebound from multi-month lows.
A 2.2 percent rebound of Banca Transilvania from a 4-month low helped Bucharest's main index firm 1 percent.
Hungary's OTP Bank shed 0.9 percent, driving Budapest's index lower by 0.8 percent, as the stock continues to seesaw near the 10,000-forint line.