Other Central European currencies like the zloty had gained late on Friday as traders sold dollars.
The euro also gained, and its strength helped currencies in the European Union's eastern wing. A delay in Britain's exit from the European Union helped sentiment.
"The market has calmed down concerning Brexit and we are also past the comments from the ECB and Fed: a calmer week starts, which alone can justified some (forint) firming after a weakening," one Budapest-based currency dealer said.
The forint rose 0.2 percent against the euro to 320.8, moving to the stronger side of its 200-day moving average for the first time in more than three weeks.
Against the zloty, the Hungarian currency rebounded from three-month lows set on Friday.
The forint underperformed in recent weeks because rising consumer prices across the region brought Hungary's annual inflation near the top of the central bank's 2 to 4 percent target range by March.
The Polish rate, confirmed at 1.7 percent on Monday, is near the bottom of its 1.5 to 3.5 percent target range.
Hungary's central bank raised one of its interest rates on March 26, but dropped its guidance of gradual monetary tightening, saying that its policy would hinge on data.
Hungarian construction output jumped by 48 percent in annual terms in February, according to figures released on Monday.
Along with a pick-up in industrial output and retail sales, the figures indicate that annual economic growth may have accelerated above 5 percent in the first quarter of the year, Takarekbank analyst Gergely Suppan said in a note.
Turnover in the region's currency markets, however, remains quite low as other emerging markets provide better news pegs for trading, dealers said.
Regional equities, mirroring their Western European peers, were range-bound and mixed, similar to government bonds.
Yields on Romanian leu-denominated bonds were mixed, after the finance ministry said late on Friday that the government planned to tap foreign markets for further issues worth 5.25 billion euros ($5.94 billion) this year and next.
The 10-year debt traded around 4.92 percent, up 1 basis point, and the benchmark overnight interbank rate was bid at its highest level in commercial banks' one-month reserve period, at 3.26 percent.