In the past three days, forces have progressed roughly 50 miles down one road toward the city and are now about a mile from its center.
The operation is part of a wide-scale offensive to retake Tikrit and Salahuddin province ordered by Iraqi Prime Minister Haider al-Abadi on March 1.
Hadi Al-Amiri, the leader of the predominantly Shiite paramilitary force Hashd Al-Shaabi, said Monday he is confident his men can crush ISIS in Iraq without the help of the U.S.-led coalition.
"We don't need it and we won't need it," said Al-Amiri. "Anyone who puts faith in the international coalition to liberate Iraq is putting their faith on a mirage. The people of Iraq will liberate this country and put an end to ISIS."
Al-Amiri's forces appear to be leading the fight for Tikrit, with support from the Iraqi army and Sunni tribesmen. Also assisting: Iran. Iran has provided advisers, weapons and ammunition to the Iraqi government. According to the Pentagon, there may be Iranians operating heavy artillery and rocket launchers as well.
"We thank them deeply for participating with us because Iran has more experience than anyone else on Earth in fighting terrorism," Al-Amiri said.
The joint effort appears to be paying off as those near the front lines point to signs that ISIS may be fracturing in some areas over the strain of attempting to function as a state.
Reports are emerging of low morale, and U.S. officials said they're seeing "anecdotal evidence of resentment and even resistance" in ISIS-controlled areas.
In addition to the push for Tikrit, Peshmerga forces south of Kirkuk retook three villages from ISIS in the past 24 hours. About 100 ISIS fighters were killed. In Syria, Kurdish forces have expanded the area they control around the city of Kobani.
After nearly 3,000 coalition airstrikes, the days of freely moving around in large formations, flying black flags and taking territory may be over for the group.
"What we've seen is ISIL pushed back both around Baghdad and in that area around Tikrit, just as we've pushed ISIL back in the north in the Kurdish areas," said Deputy National Security Adviser Ben Rhodes, using another acronym for the radical Sunni militant group. "The amount of territory ISSL holds inside Iraq has been shrinking."
Tikrit, best known to Westerners as the birthplace of former Iraqi dictator Saddam Hussein, fell to ISIS in June. There have been several failed attempts to recapture the city since the second half of 2014. If Iraq regains control of the city, it could mean retaking Mosul -- a city 10 times bigger -- is possible.
The offensive involves around 30,000 fighters.