ANALYSIS-Saudi wants bigger role in Iraq to counter Iran

* Riyadh believes Maliki is too close to Iran

* Saudi-Iraqi relations frosty since Saddam fell in 2003

* Saudi firms lag Turkish, UAE, Iran rivals in Iraq market

By Ulf Laessing

BAGHDAD, Aug 2 (Reuters) - Saudi Arabia wants to play a bigger role in Iraq to counter Iran's growing influence during a political stalemate in Baghdad, and to help Saudi companies to catch up with regional rivals in opening up the Iraqi market.

But Riyadh, a bastion of Sunni Islam, is hoping that Iraq's Shi'ite Prime Minister Nuri al-Maliki does not make a comeback after inconclusive elections created a power vacuum,believing that he is too close to the Shi'ite leadership in Tehran.

"The Saudis feel that Maliki is a man of Iran," said Saudi political analyst Khaled al-Dakhil. "It seems to me the king does not want to open an embassy as long as Maliki is there. He's waiting for another prime minister or government."

The world's top oil exporter is trying to contain the regional influence of Iran, which has clout among majority Shi'ites in Iraq, and shares U.S. concerns that Tehran wants to develop nuclear weapons, a charge Tehran denies.