BERLIN (Reuters) - One of the leading figures in Chancellor Angela Merkel's conservative sister party, the Christian Social Union (CSU), pleaded on Tuesday for an "orderly" exit of Greece from the euro zone, saying it was the best option for all concerned.

The comments from Markus Soeder, regional finance minister of the Bavarian CSU, underscore the depth of frustration with Greece in Merkel's conservative camp and how difficult it would be for her to reverse course and offer Athens new concessions to keep them in the euro.

Although the CSU has taken a tougher line on Greece than Merkel's own party, the Christian Democrats (CDU), the conservative backlash against Athens has broadened since Greek Prime Minister Alexis Tsipras broke off bailout talks last week and called a referendum.

Greece is widely expected to miss a 1.6 billion euro payment to the IMF on Tuesday, effectively putting them in default.

Soeder told Deutschlandfunk radio that an "orderly, judicious and considered exit plan would be the best path for both sides", sharply criticizing Tsipras for playing with Europe and his own people.

If Tsipras remains in office, Soeder said a so-called "Grexit" appeared "unavoidable". Even if Greeks vote in favor of a bailout in the referendum, which is scheduled for Sunday, Soeder argued against making any more concessions to Athens.

(Reporting by Noah Barkin; Editing by Gareth Jones)