Bakara market was also bombed on Tuesday
At least 50 people have reportedly been killed in clashes in the Somali capital Mogadishu and the port of Kismayo.
Some 30 people have been killed in two days of fierce fighting between Islamists and a clan militia in Kismayo, a BBC reporter says.
Some mortars landed near the compound of President Abdullahi Yusuf, who is currently out of the country.
Another landed near a mosque in the busy Bakara market, killing at least six people, a witness told the BBC.
At least 3,000 people are reported to have fled the fighting around Kismayo.
Witnesses say that after the mortars landed in Bakara and near the president's compound, government troops and their Ethiopian allies opened fire, killing several civilians.
One witness told the BBC that the mortar landed outside the mosque as people were preparing for prayers.
He said that the wounded could not be evacuated for some time because of the horrific scenes.
Ethiopian troops entered Somalia in December 2006, to oust Islamist forces from Mogadishu.
Somalia has been without a functioning national government since 1991 and has suffered ongoing civil strife.
The UN's World Food Programme is expanding its programme to feed 2.4 million people in Somalia by the end of the year.