According to the New York Times:
Shiite militia leaders said that their fighters made up more than two-thirds of the pro-government force of 30,000, and that the Iranian spymaster Maj. Gen. Qassim Suleimani was helping to lead from near the front lines.
Alongside them were advisers and troops from Iran’s Revolutionary Guard Corps, operating artillery, rocket launchers and surveillance drones, according to American officials…
But progress appeared slow in the push against Tikrit on Tuesday, with no breakthrough in the Iraqi coalition’s efforts to enter the city. Iraqi military officials said they had reached the outskirts of Al Dour, just south of the city, and were advancing slowly after freeing 13 police officers held there by the Islamic State.
Mohammad al-Turkomani, a leader in the militias known as the “popular mobilization” forces, said that with American participation in Tikrit, “we would have moved twice as fast.”
For their part, Iraqi officials increasingly complain that American support has not been as robust as Iran’s. Many Iraqis resent what they see as American squeamishness about the militias, which by all accounts have been crucial to holding back the Islamic State after regular army units fled its assault.
“Americans consider us a militia that does not represent the government, while we are defending the country and helping the government,” said Mueen al-Kadhimy, a leader in the Badr Organization, a prominent militia. “We are the people of Iraq.”COMMENTARY: The Battle of Tikrit is expected to be a tough slog for Iraq and the Iran-led coalition against ISIL, without U.S.-led coalition tactical air power.
Much is on the line for the Iranians in terms of regional martial regard. Their coalition forces are said to be providing 2/3 of the said 30,000 force committed to the larger military operation.
The Iranians have a previous set of limited military successes in Iraq; before that more mixed results in Syria, where they've at a minimum been able to maintain the Syrian Arab Republic against a field of adversarial forces.
In the Battle of Tikrit, the Iran-led coalition and ISF forces appear to possess advantages of overwhelming numbers and materiel. Envisioned battle duration is for ten days or beyond, with logistics identified as a potential determining factor for whether or not the battle devolves into a relatively lengthy siege.
Iran-supplied Fath Safir ("Ambassador") tactical vehicle fitted with 107 mm MLRS
Photo of IRGC-QF Commander Soleimani, said taken near the front during Battle of Tikrit