The Iraqi Counter Terrorism Service (CTS) is an elite special forces unit that has spearheaded assaults in most key battles against IS

Iraqi forces battling jihadists in Mosul reached the Tigris River that divides the city Sunday, a key step and a first since the launch of a huge operation in mid-October.

The Islamic State group was on the back foot in Mosul after a week of significant gains for Iraqi forces but pressed a deadly campaign of bombings in Baghdad, where two more attacks killed 18 people.

Elite Counter-Terrorism Forces (CTS) took control of the eastern end of the southernmost bridge in Mosul, a morale-booster in a 12-week-old operation that has encountered many difficulties.

CTS forces "reached the Tigris River from the eastern (side) of the fourth bridge," Sabah al-Noman told AFP. The news was also confirmed by Iraqi army Staff Lieutenant General Abdulamir Yarallah.

Tens of thousands of Iraqi forces launched an offensive on October 17 to retake Mosul, the last major urban centre in Iraq still controlled by the group that seized around a third of the country in 2014.

Several areas around the city, Iraq's second largest, were swiftly reconquered, but the elite forces that pushed into the streets of Mosul itself have faced stiffer than expected resistance.

In late December, the federal advance inside the city had slowed to a crawl but a fresh coordination effort between CTS and other forces gave fresh impetus to the operation.

Iraqi forces, backed by increased support from the US-led coalition that has carried out the bulk of air strikes against IS and deployed military advisers on the ground, made rapid progress in the first week of 2017.

Their push to the banks of the Tigris River on Sunday marks a symbolic and tactical victory for the Iraqi forces but they have much work left to do to take full control of Mosul's eastern side.

Having eyes on the river should further complicate IS's already reduced ability to resupply the eastern front with fighters and weapons from the west bank, which it still firmly controls.

Commanders had predicted when the operation, Iraq's largest in years, was launched nearly three months ago that the eastern side of the city would be easier to retake.

- Baghdad bombings -

But die-hard jihadist fighters, estimated at around 5,000 to 7,000 before the start of the offensive, fought back with sniper fire, booby-traps and a seemingly endless supply of suicide car bombs.

The continued presence in the city of hundreds of thousands of civilians -- either forced to stay by IS or reluctant to leave their homes for crowded and cold displacement camps -- has impeded the federal advance.

Baghdad and partnering aid organisations had predicted an exodus of civilians in the first weeks of the operation but the flux of fleeing Mosul residents was more limited than expected.

According to the United Nations, more than 135,000 people have been displaced since the start of the operation to retake Mosul, a significant proportion of them from outlying areas.

Iraqi Prime Minister Haider al-Abadi had promised that his forces would rid Iraq of IS by the end of 2016 but later said that eliminating the jihadists would take several more months.

The western bank of the city is slightly smaller than the east but more densely-populated and includes neighbourhoods that are seen as bastions of support for the Islamic State group.

The jihadists, vastly outnumbered and outgunned in Mosul by federal forces and their allies, have launched a number of diversionary attacks over the past three months.

They also appear to have ramped up suicide bomb attacks in the capital, where at least 18 people were killed in two separate blasts near markets on Sunday.

The first attack struck the main wholesale vegetable market in Baghdad, which lies in the frequently-targeted, overwhelmingly Shiite neighbourhood of Sadr City.

"A soldier at the gate of Jamila market opened fire on a suicide car bomb after noticing a suspect vehicle but the terrorist blew up his car," interior ministry spokesman Saad Maan said.

At least 12 people died in the explosion while another six Iraqis were killed in a second attack at a market in the Baladiyat area, security and hospital officials said.

The explosions were the latest in a string of attacks that have left close to 100 people dead since New Year's Eve.