That puts less pressure on central banks in central Europe to rapidly tighten monetary policy.
Hungarian markets had been particularly nervous ahead of the ECB's statements after its policy meeting on Thursday.
Regional markets have mostly calmed down this month after a sell-off swept emerging markets in May amid a rally of the dollar and US yields.
But Hungary's relatively expensive bonds, which were in the centre of the May sell-off, have been hit again.
The 10-year yield rose 50 basis points in the past week to a 15-month high of 3.58 percent at one stage on Thursday as rumours about comments made behind closed doors by a senior rate setter raised questions about the Hungarian central bank's commitment to keeping interest rates low for years.
Separately, central banker Gyula Pleschinger told Reuters on the sidelines of a conference on Thursday that he saw no reason for now for the bank to change its easing bias.
After Pleschinger's comments, the forint fell to 323.35 against the euro, its weakest level since early 2015.
But it rebounded to 321.9 by 1350 GMT, after the ECB's news conference while the yield on Hungary's 10-year bonds fell 20 basis points to 3.38 percent.
"This is because the ECB comments were more dovish than expected," one Budapest-based fixed income trader said.
Budapest's main equities index also rebounded from a six-week low, gaining 1 percent and driven by a 2.8 percent rise in OTP Bank shares.
The NBH will meet on Tuesday and its comments on the recent market turmoil and its policy guidance will be closely watched, traders said.
Before the ECB's statements, market jitters had reached short-term interest rates.
Hungary's debt management agency AKK cut its 12-month Treasury bill offer, an unusual move at Hungarian debt auctions, as demand was weak. Even with the cut, the average yield jumped to 0.4 percent from 0.28 percent two weeks ago.
A 26-week bill auction in Prague also saw a slump in demand, even though the Czech central bank has started raising rates, in contrast with Hungary, and may deliver another one soon.