BAGHDAD  A wave of American companies have been arriving in Iraq in recent months to pursue what is expected to be a multibillion-dollar bonanza of projects to revive the country’s stagnant petroleum industry, as Iraq seeks to establish itself as a rival to Saudi Arabia as the world’s top oil producer.

Since the 2003 American-led invasion, nearly all of the biggest reconstruction projects in Iraq have been controlled by the United States. But many rebuilding contracts are expected to be awarded as soon as this month for drilling hundreds of new wells, repairing thousands of miles of pipeline and building several giant floating oil terminals in the Persian Gulf, and possibly a new port.

The contracts will be administered either directly by the Iraqi government or as part of Baghdad’s oversight of international oil companies that have signed agreements during the past few months to develop the country’s most promising oil fields.

There are misgivings, however, about Iraq’s ability to adequately monitor contracts that could total $10 billion over the next five years. The concerns have been heightened by the prominent role expected to be played by American companies that have been criticized in the past by United States government auditors and inspectors for overcharging by hundreds of millions of dollars, performing shoddy work and failing to finish hundreds of crucial projects while under contract in Iraq.