Thousands of Iraqi soldiers and Shiite militiamen sought to seal off Islamic State fighters in Tikrit and nearby towns on Tuesday, the second day of Iraq's biggest offensive yet against a stronghold of the radical Sunni Islamist militants.

Iranian military commander Qassem Soleimani, who has helped coordinate Baghdad's counter-attacks against Islamic State since it seized much of northern Iraq in June, was overseeing at least part of the operation, witnesses said.

His presence on the frontline highlights neighboring Iran's influence over the Shiite fighters who have been key to containing the militants in Iraq.