By Micah Maidenberg

Novartis AG, a subsidiary of the pharmaceutical company and a unit of eyecare company Alcon Inc. have agreed to pay about $347 million in fines to resolve claims they violated the Foreign Corrupt Practices Act, officials and Novartis said Thursday.

A Novartis unit for Greece allegedly tried to bribe employees of state-owned and state-controlled hospitals and clinics, among other alleged violations, the Justice Department said Thursday.

An Alcon subsidiary allegedly made and falsely recorded improper payments in Vietnam, according to prosecutors.

The Novartis business for Greece agreed to pay a criminal penalty of $225 million, the Justice Department said.

"Today's resolutions contain no allegations relating to any bribery of Greek politicians, which is consistent with what Novartis found in its own internal investigation," Novartis said in a statement.

The Alcon subsidiary will pay a criminal penalty of about $8.9 million, the Justice Department said.

"We are pleased with the completion of the investigation and settlement," Alcon said in a statement.

Alcon merged with Novartis in 2011 and was spun off from the company last year, according to the Securities and Exchange Commission.

Novartis will pay more than $112 million to the SEC to settle charges with the agency that it violated the books and records and internal accounting controls provisions of the Foreign Corrupt Practices Act, the commission said.

"With today's agreements, all outstanding FCPA investigations into Novartis are now closed," the Swiss pharmaceutical company said.

Write to Micah Maidenberg at micah.maidenberg@wsj.com