(CNN) -- Kenya's military controls half of the Somalian port city of Kismayo as it tries to drive out the al Qaeda-linked militant group Al-Shabaab from one of its last strongholds, a military spokesman said Saturday.
Kenyan and Somali ground forces are in control of the northern part, which is the old city, after a day and a half of fighting, spokesman Cyrus Oguna told CNN.
They are consolidating the areas they have gained before moving into the south, where the Islamic militant group is believed to be, he said. The military launched airstrikes against the group Saturday.
"Al-Shabaab has not been able to offer any resistance whatsoever to the ground forces since the ground forces landed there yesterday, and the whole of yesterday and the good part of today they have (suffered) heavy casualties," Oguna said.
The Kenya Defense Forces inflicted "massive destruction" on Al-Shabaab's infrastructure Saturday, using jets and helicopter gunships to destroy three of the group's bases, according to the military's official Twitter account. "Great care and caution has been exercised to avoid collateral damage," it said.
But in a series of posts Saturday on a Twitter account often used by Al-Shabaab, the group said the Kenyan military is "waging a losing battle" in Kismayo. It said mujahedeen forces ambushed Kenyan troops 30 km (18 miles) west of Kismayo, destroying three vehicles and killing dozens of troops in a two-hour battle.
Oguna said those reports are "pure propaganda."
"There has been no major ground forces engagement," he said.
Kenya's military makes up the majority of troops in an African Union offensive to drive Al-Shabaab out of Somalia, where the group has long tried to overthrow the government.
Al-Shabaab has suffered setbacks in the fight, including losing control of much of the capital, Mogadishu, last year. That made Kismayo even more critical for the group, which uses the port to profit from the illegal charcoal trade and smuggling operations.
Thousands of civilians fled the city this month as fighting loomed, according to the U.N. refugee agency. It said that Somalis were leaving in minibuses, in trucks and on donkey carts.
"Great care and caution has been exercised to avoid collateral damage," the Kenyan military said Saturday.
Since crossing into Somalia in October, Kenyan commanders and politicians have stated more than once that capturing Kismayo was the ultimate aim of their operation.
The military's operation to take Kismayo began with airstrikes and naval gun support three days before the ground troops arrived, Oguna said.
Twitter postings Friday from Kenya's prime minister and deputy prime minister congratulating the military on capturing Kismayo actually referred to the ground forces' arrival in the city, Oguna said.