Tudose's Social Democrat Party (PSD) withdrew its backing for him in an overwhelming vote on Monday. He had been embroiled in a row with the party's powerful leader Liviu Dragnea.

Romanian equities shed half a percent by 0944 GMT, underperforming Central European peers.

Tudose's resignation does not signal a change in economic policy but adds to Romania's political instability caused by in-fighting and corruption scandals. The ruling party's leaders will meet on Tuesday to discuss choices for a new prime minister.

President Klaus Iohannis "once more holds the wild card of PM designation", Erste Group analyst Horia Braun-Erdei said in a note.

If Iohannis were to propose his own candidate instead of accepting the PSD's nominee, Romania could see early elections, Braun-Erdei said.

"The next few days will tell whether there will be a way out of this conundrum or whether we are heading for a full-fledged political crisis," the note said.

The leu eased 0.4 percent against the euro to 4.6575, slightly off the day's low of 4.661 which was close to its end-2017 record low at 4.68.

A surge in wages has led to worries that Romania's economy would overheat. The Romanian central bank delivered its first interest rate hike in a decade on Monday last week to fight a surge in inflation.

"The leu's reaction to the resignation seems muted," said one trader in Bucharest. "Still, there is no reason for it to firm and every reason for it to remain weak."

Politics in Central Europe's fast-growing economies generally had little influence in markets in the past year.

Czech Prime Minister Andrej Babis's minority government is expected to lose a confidence vote in parliament due at around 1300 GMT.

The Czech crown was still steady at 25.518 against the euro.

Even if Babis loses the confidence vote, his government will stay in office until a new one is formed and he may end up leading any new government.

He requested lawmakers on Tuesday to lift his parliamentary immunity so he can face allegations of fraud, but he remains popular.

Czech government bond yields were bid higher by a few basis points.

The Czech finance ministry said on Monday that it would double the maximum planned offer at Wednesday's scheduled  auction of bonds maturing in 2023, 2028 and 2033.