The forint traded at 323.48 versus the euro at 1423 GMT, off four-week highs set earlier in the session at 322.7, but firmer by half a percent from Monday.
The NBH kept interest rates at record lows, but said it would phase out its monetary policy interest rate swaps and its mortgage bond buying programme by the end of 2018.
It retained its foreign currency swaps providing forint liquidity and said it would adjust monetary policy by using them in the right combination with the interest rate corridor around its benchmark rate.
The changes will allow the bank to act if inflation trends make it necessary, while "the bias of monetary policy has not changed," NBH Deputy Governor Marton Nagy told a news conference.
The bank's signals that it is prepared to move away from its ultraloose policy is positive to the forint, one Budapest-based currency dealer said.
"We see the end of the tunnel," the dealer said.
It will take a few more days for the market to digest Tuesday's announcements, one Budapest-based fixed income trader said.
A rise in domestic savings and expected European Union funding inflows make a fast rise in interest rates unlikely, Takarekbank analyst Gergely Suppan said in a statement.
Hungary's 10-year government bonds traded at a yield of 3.68 percent, off their midday fixing of 3.73 percent which was its second highest level in the past three years.
Nagy also said that based on the current inflation outlook, no interest rate change was justified until the middle of 2019, and that bigger policy decisions could be expected on a quarterly basis, depending on the bank's inflation report.
The NBH did not increase its inflation forecasts in the main figures of the September report revealed on Tuesday, despite some expectations for a rise.
Inflation has picked up across Central Europe in the past months.
Worried over the rise, the Czech central bank is expected to deliver its third interest rate hike in a row next week.
The Czech crown set a 5-month high at 25.42 against the euro on Tuesday. At 1423 GMT it traded at 25.43, firmer by 0.1 percent from Monday.
The leu, meanwhile shed a quarter of a percent to trade at 4.652. The zloty was a shade firmer against the euro on the strong side of the 4.3 psychological line.