The number of jihadist car bomb attacks against Iraqi forces advancing in Mosul has fallen sharply to just a few a day, a top special forces commander said Tuesday.

Major General Maan al-Saadi of the elite Counter-Terrorism Service, which has done much of the fighting in east Mosul, said the Islamic State group's defence of its last major Iraqi bastion was weakening.

"Car bombs have been a key component" of IS's defence system since a broad offensive, Iraq's largest military operation in years, was launched on October 17 to retake Mosul, Saadi told AFP inside the city.

"At the beginning, they launched many car bombs, now much fewer. There are one, two or three a day, never more than 10," he said. "In the first phase, they used more than 50 a day."

Many of those attacks were conducted by suicide bombers who ram their explosives-laden vehicles into federal forces.

A fresh push that started on December 29 has seen Iraqi forces, with increased backing from the US-led coalition, make significant gains in the eastern side of the city.

The west bank of Mosul remains under full IS control however and was seen before the launch of the offensive as the hosting the city's most diehard jihadists.

A Pentagon spokesman in Washington had spoken of the same trend on Monday.

"We see fewer and fewer VBIED than we had previously in Mosul," Navy Captain Jeff Davis said, using the acronym for vehicle-borne improvised explosive devices.

Iraqi forces advancing in east Mosul on Sunday reached the Tigris River that splits the city for the first time.

Combined with coalition air strikes on the bridges in central Mosul in recent weeks, the Iraqi push makes it very difficult for IS to resupply its eastern front.

Another CTS commander said on Monday that the full recapture of east Mosul would be completed in a matter of days.

The next phase of the nearly three-month-old operation will involve moving into the streets of west Mosul.

A variety of Iraqi forces are positioned near the airport, which lies at Mosul's southern entrance but west of the river, in desert areas to the west and on the northern edges of the city.