Iran has actively and visibly supported Baghdad's biggest operation yet against the ISIL group, General Martin Dempsey said.
The Takfiri group's footprint in Iraq has been shrinking steadily since federal and volunteer forces went on the counter-offensive roughly six months ago.
"Iraqi security forces and tribal fighters from the Anbar region have successfully cleared Al-Baghdadi of ISIL, retaking both the police station and three Euphrates River bridges," the U.S. military said.
An offensive was also launched this week to recapture Gurma, another town in Anbar which is just 10 kilometers (six miles) from the ISIL stronghold of Fallujah and less than 30 kilometers from Baghdad airport.
"Gurma will soon be liberated totally, our forces are on the edge of town," a statement from Baghdad operations command said.
It claimed that 73 Takfiris were killed in the first two days of fighting and a number of bombs defused.
An official with the religious authority in the holy city of Najaf, where many Shias want to be buried and which has the world's largest cemetery, said the bodies of 64 fighters killed in the Tikrit battle and elsewhere had been brought in since March 4.
Undated footage surfaced on the Internet Saturday of the bodies of eight men described as pro-government volunteers hanging from a bridge in Hawija, 75 kilometers north of Tikrit.
Iraqi forces spent the operation's first days clearing outlying areas and are now closing in on Tikrit itself, as well as the towns of Al-Alam and Ad-Dawr.
Tikrit is the home town of executed dictator Saddam Hussein and Ad-Dawr that of Izzat Ibrahim al-Duri, the most senior member of his regime still at large.
"There are fierce clashes around Ad-Dawr, with army aircraft providing support against the threat of snipers and car bombs," an army lieutenant colonel told AFP.
Dempsey, speaking to reporters aboard his plane en route to Bahrain and Iraq, said it was only a matter of time before ISIL was defeated in Tikrit.
"The numbers are overwhelming," he said, adding that "hundreds" of ISIL terrorists were facing an estimated 23,000 government and allied forces.
The terrorists have been responding by ramping up what UNESCO has called cultural cleansing, destroying heritage treasures one after the other.

Destruction of Hatra
ISIL terrorists have destroyed ancient remains of the 2,000-year-old city of Hatra in northern Iraq, the tourism and antiquities ministry said on Saturday.
An official told Reuters that the ministry had received reports from its employees in the northern city of Mosul that the site at Hatra had been demolished on Saturday.
The official said it the ministry had not received any pictures showing the extent of the damage at Hatra, which was named a world heritage site in 1987.
But a resident in the area told Reuters he heard a powerful explosion early on Saturday and said that other people nearby had reported that ISIL militants had destroyed some of the larger buildings in Hatra and were bulldozing other parts.
Hatra lies about 110 km (70 miles) south of Mosul, the largest city under ISIL control. A week ago the militants released a video showing them smashing statues and carvings in the city's museum, home to priceless Assyrian and Hellenistic artifacts dating back 3,000 years.
On Thursday they attacked the remains of the Assyrian city of Nimrud, south of Mosul, with bulldozers. The United Nations cultural agency UNESCO condemned the actions as "cultural cleansing" and said they amounted to war crimes.
Hatra dates back 2,000 years to the Seleucid empire which controlled a large part of the ancient world conquered by Alexander the Great. It is famous for its striking pillared temple at the center of a sprawling archaeological site.
Saeed Mamuzini, spokesman for the Mosul branch of the Kurdish Democratic Party, said the militants had used explosives to blow up buildings at Hatra and were also bulldozing it.
The antiquities ministry said the lack of tough international response to earlier ISIL attacks on Iraq's historic sites had encouraged the group to continue its campaign.
"The delay in international support for Iraq has encouraged terrorists to commit another crime of stealing and demolishing the remains of the city of Hatra," it said in a statement.
Archaeologists have compared the assault on Iraq's cultural history to the Taliban's destruction of the Bamyan Buddhas in 2001. But the damage wreaked by ISIL, not just on ancient monuments but also on rival Muslim places of worship, has been swift, relentless and more wide-ranging.
Last week's video showed them toppling statues and carvings from plinths in the Mosul museum and smashing them with sledge hammers and drills. It also showed damage to a huge statue of a bull at the Nergal Gate into the city of Nineveh.
Last July ISIL destroyed the tomb of the prophet Jonah in Mosul. It has also attacked Shia places of worship and last year gave Mosul's Christians an ultimatum to convert to Islam, pay a religious levy or face death by the sword. It has also targeted the Izadi minority in the Sinjar mountains west of Mosul.