Political uncertainty weighed on stock markets globally, and equities in the eastern states of the European Union fell in line with Western peers.
Investors also used the negative sentiment for some profit-taking.
Budapest's main index hit record highs last week and now dances around the key 35,000-point mark, and in Bucharest whose index is retreating from its highest levels since early 2008.
Budapest shed 0.6 percent by 0939 GMT even though road transport firm Waberer's International announced that it planned to raise 50 million euros ($56 million) in fresh capital in a
initial public offering (IPO), and listing in Budapest.
Apart from Warsaw, Central Europe's biggest bourse, IPO's are rare in the region.
Successful IPO's were Moneta bank in Prague last year and cable and internet provider DIGI Communications N.V in Bucharest last month.
Raiffeisen's Polish unit and debt collector GetBack consider IPOs in Warsaw.
Waberer's planned listing could make it the fifth biggest stock on the Budapest Stock Exchange and fuel foreign investors' interest in the bourse, market participants said.
Waberer's is one of the biggest road haulage companies in the EU.
It will face difficulties due to Britain's move to quit the EU, tightening regulations on the industry in Europe and a rise in administrative costs, Equilor brokerage analyst Monika Kiss told Reuters.
But it is helped by economic pick-up in Europe and in Hungary, relatively low wages in Central Europe and a decline in fuel prices.
Crude prices were slightly lower, though off intra-day lows on Tuesday, with the tension around Qatar raising questions over its agreed production quota.
The stocks of Polish oil group PKN Orlen PKN.WA> and refiner Lotos rose 2.4 percent, and 3.1 percent, respectively, keeping Warsaw's main index in the positive despite a fall in other shares.
Bucharest's index fell 1.1 percent, pulled down partly by a 7.1 percent plunge in the stocks of power grid operator Transelectrica which traded ex-dividend, has a newly appointed management and reported disappointing first-quarter results recently.
Poland's 10-year government bond yield dropped 2 basis points to 3.1655 percent ahead of a meeting of the Polish central bank on Wednesday.
The bank is likely to keep interest rates on hold until it raises them in the third quarter of 2018, a Reuters poll found last week, a quarter later than the previous sounding.