BUCHAREST, Aug 6 (Reuters) - Romanian Prime Minister Victor Ponta reshuffled his cabinet on Monday after his interior minister quit, and the central bank governor warned that Ponta's feud with the president could weaken the leu and make it hard to finance the budget.

Ponta's Social Liberal Union (USL) is embroiled in a battle to oust suspended President Traian Basescu that has stalled policymaking, drawn criticism from abroad and raised concerns over Romania's IMF-led aid deal.

A July 29 referendum on whether to impeach Basescu won 88 percent support but the turnout was below the 50 percent needed to make it valid.

The Constitutional Court has asked to see the voters list at the time of the referendum before ruling on the true size of the electorate and the validity of the vote, a ruling it was supposed to give last week but has put off to Aug. 31.

Ponta suffered a blow early on Monday when Interior Minister Ioan Rus quit, citing political pressure in connection with the court's work on the referendum.

Ponta moved quickly, naming party loyalists Mircea Dusa and Titus Corlatean as new interior and foreign ministers, judge Mona Pivniceru as justice minister, and new development and parliamentary affairs heads, saying he wanted to change the cabinet's strategy.

He said his co-party leader and interim president Crin Antonescu had approved his nominations and they would be sworn in later on Monday.

The minister in charge of liaising with the business sector, Lucian Isar, also resigned later in the day for personal reasons, and was to be replaced, a senior USL member told reporters.

Before the reshuffle, central bank governor Mugur Isarescu urged politicians to reduce the tension that has driven the leu currency to record lows and lifted state borrowing costs.

"We are dependent on international markets and they penalise (us) dramatically," Isarescu told a news conference as he presented the bank's quarterly inflation report.

"For now this shows on the exchange rate but it will (also) show in funding costs."

PRESSURE ON RUS

Rus, explaining his departure, suggested both sides in the political feud had tried to benefit from the process.

"There have been countless pressures on me and the ministry, countless discussions by Romanian politicians, starting with Traian Basescu and moving on to Crin Antonescu," Rus said.

"From our point of view, it is unacceptable."

The updated voters list could show a lower number of registered voters than thought, pushing the recorded turnout of 46 percent closer to the 50 percent plus one required for a valid referendum.

But analysts said the turnout was still very likely to remain below 50 percent making the referendum invalid.

"Legally or statistically I don't see how the permanent voter lists can be changed significantly," said Adrian Basaraba, a political science professor at the University of Timisoara.

"I think the reshuffle was meant to distract attention and maybe soften the negative impact on the USL of the resignation of Ioan Rus, who is making accusations of political pressure."

The leu rebounded by 1.4 percent against the euro from a record low hit on Friday, and dealers the central bank had intervened to prop it up. Dealers say the bank often intervenes in the currency market to prevent sharp swings.

Ponta's drive to oust Basescu, who he accuses of abusing his position and blocking the government's policies, drew harsh criticism from the European Commission, Berlin and Washington, which said his cabinet had undermined democracy and rule of law.

Ponta's USL looks set to hold on to power after a general election in the autumn, but the country of 19 million could suffer from policy deadlock - possibly threatening Romania's ability to fulfil its obligations to the IMF - if Basescu stays and the two sides remain at odds. (Additional reporting by Ioana Patran; Editing by Michael Winfrey and Sophie Hares)