A rise in US rates would make Central European assets relatively less attractive.
The zloty gave up part of Monday's gains against the euro and traded at 4.0 at 1312 GMT, weaker by 0.3 percent, while the forint shed 0.5 percent to 301.5.
The forint has been dancing around 300 and the zloty around 4.0 for weeks, clinging to strong gains since the end of 2014: five percent for the forint and seven percent for the zloty.
Poland has signalled that its rate cut cycle is over and the zloty is widely expected to extend its gains. A weak zloty could hurt the 550,000 Poles holding mortgages denominated in the Swiss franc.
Hungary, Serbia and Romania could continue to ease monetary policy. The Czech central bank's board has discussed alternative policy tools including negative interest rates, Governor Miroslav Singer told Reuters.
Polish government bond yields are well above euro zone levels. The 5-year yield rose 9 basis points to 2.07 percent, offering a 156 basis point premium over the corresponding Spanish yield.
Poland priced a Swiss franc bond issue at a yield of minus 0.2 percent, becoming the first emerging market sovereign to sell a bond at a negative yield, the Reuters financial news service IFR said.
Equities mostly tracked Western European peers lower on Tuesday, but Poland's share index was flat, helped by gains in banking stocks after strong first-quarter earnings from BZ WBK and Bank Millennium.
Their results indicated that the problem of Swiss franc loans has caused less damage to the Polish banking system than expected.
Analysts say that if Polish banking stocks continue to perform well then Warsaw's main stock index, up 10 percent this year, could rise further and narrow the gap with Budapest which has surged 39 percent.
Shares of Hungarian oil group MOL rose 3.3 percent, lifting Budapest's main index by half a percent.
It tracked the recent gains of regional peers OMV and Poland's PKN Orlen, which is trading near record highs, said Monika Kiss, analyst at brokerage Equilor in Budapest.