* Shareholders fear Greece probe could be longterm problem
* Novartis pledges action if unethical behaviour emerges
* Athens court has asked Switzerland for help in probe (Adds detail about request from Athens court for Swiss assistance)
By John Miller
ZURICH, March 2 (Reuters) - Several Novartis shareholders urged the Swiss drugmaker to improve its oversight of staff on Friday, amid a widening inquiry into allegations that managers paid bribes to doctors and public officials in Greece.
Greece's parliament voted last week to investigate 10 politicians, in addition to an ongoing probe of the Basel-based company after a raid on its offices in Athens a year ago.
Mike Moran of Suishare, a small not-for-profit shareholders group that focuses on business ethics, told Novartis's board on Friday he was worried the investigation could prove to be a long-term headache for the company.
"I think the Greek thing will be the swamp that keeps on giving," Moran said at the company's annual shareholder meeting.
Other investors also expressed concern, with one calling for executives to exert greater "moral influence" after a series of costly legal problems.
Since 2015, Novartis has paid out hundreds of millions in settlements and fines as a result of kickback allegations in South Korea, the United States and China.
"Corruption cannot be allowed to become a tradition," said Veronika Hendry, president of the sustainable investing proxy group Actares.
The Swiss Attorney General's (AG) office said on Friday that an appeals court in Athens had submitted a request for assistance, adding the request is being reviewed. No criminal proceedings have been opened in the matter in Switzerland, an AG spokeswoman said in a statement via email.
Novartis, which on Sunday condemned violence at its Athens office and called on Greek police to protect its employees, has said it will take "fast and decisive action" should evidence of unethical or illegal behavior emerge.
Chairman Joerg Reinhardt underscored that pledge on Friday.
"We will continue to do whatever we can to clarify the situation," Reinhardt said. "If anybody was responsible for any misdeed, we will act accordingly."
Questioned about Novartis's pay system which includes bonuses for meeting targets, Reinhardt acknowledged risks associated with monetary rewards but said he and other officials including new Chief Executive Vas Narasimhan carefully scrutinize what employees do with incentives to prevent abuses.
"I know Mr. Narasimhan has a very close eye on this," he said.
Shareholders overwhelmingly approved a pay plan for Novartis executive committee and board members including Narasimhan that could total 100 million Swiss francs ($107 million) for 2018-2019. They also approved the other board proposals.
Novartis shares were down 1.2 percent at 1330 GMT, mirroring the SIX Swiss Exchange. ($1 = 0.9350 Swiss francs) (Reporting by John Miller Editing by Mark Potter and Alexander Smith)