(Changes details of majority in par 4)
* Democratic Left party expels two lawmakers over probe call
* Greek govt majority cut to 164 in 300-seat parliament
ATHENS, Jan 7 (Reuters) - The smallest party in Greece's government expelled two lawmakers on Monday for backing an investigation into a ruling party leader over his handling of a list of possible tax cheats, cutting the fragile coalition's majority in parliament.
Democratic Left lawmakers Odysseas Voudouris and Paris Moutsinas supported a call by the opposition Syriza party to look into Socialist leader Evangelos Venizelos's role in a scandal over the so-called "Lagarde list" that names rich Greeks who stashed money abroad.
"What is now clear is that the two deputies not only express a different opinion but also support a different political plan," the party said in a statement confirming their expulsion from its parliamentary group.
The expulsions cut the ruling coalition's majority, leaving it with 164 lawmakers in the 300-seat parliament.
The Lagarde list - and the failure of successive governments to investigate those named on it - has provoked outrage among austerity-hit Greeks furious that authorities have done little to crack down on tax evasion by the wealthy elite.
Prime Minister Antonis Samaras's government has rejected calls to look into accusations that Venizelos - a former finance minister who heads the PASOK party - has not done enough to pursue the alleged tax cheats.
The government has instead focused on the role of Venizelos's predecessor at the finance ministry, George Papaconstantinou.
The government last month backed an investigation into Papaconstantinou after prosecutors found names of his relatives were deleted from the list when he was in office.
The Greek government obtained the list from French authorities in 2010, but little was heard of it until officials revealed its existence late last year.
It was then published by a Greek magazine, whose editor was immediately arrested and then acquitted on charges of violating privacy laws.
The list, named after IMF chief Christine Lagarde who was French finance minister at the time, has become a symbol of both the tax evasion partly blamed for pushing Greece to a financial crisis and the reluctance of authorities to go after evaders.
(Reporting by Renee Maltezou and Lefteris Papadimas; Writing by Deepa Babington; Editing by Andrew Heavens)