Kenyan troops with aerial support are continuing their advance into Somalia towards a town held by al-Shabab 120km (75 miles) from the border.
The Kenyan government wants to push the militants away from its border following a spate of kidnappings it blames on the Islamist insurgent group.
Kenyan army spokesman Maj Emmannuel Chirchir said the advance to Afmadow had been slowed by muddy terrain.
Meanwhile, three civilians have died in a Mogadishu car bomb, witnesses say.
The BBC's Mohammed Dhore in the city says the suspected suicide car bomb went off outside the former ministry of foreign affairs, which is now unoccupied.
Earlier this month, al-Shabab militants carried out a suicide bombing in Mogadishu which killed at least 70 people.
The militant group has warned of attacks in Kenya unless the troops withdraw and the blast occurred as Kenya's defence and foreign ministers, Yusuf Haji and Moses Wetangula, were at the city's main airport for talks with Somali government officials.
Al-Shabab, which controls much of southern Somalia, has denied carrying out any abductions.
It is locked in a battle with the transitional government for control of the parts of the country which are currently outside its power, particularly the capital, Mogadishu.
The UN-backed government in Mogadishu has refused to admit that the Kenyan troops are inside Somalia.
But BBC East Africa correspondent Will Ross says sources indicate that Somali government troops are working in tandem with the Kenyans in order to attack the al-Shabab-controlled areas.
Eyewitnesses say al-Shabab officials have forced truck owners to hand over their vehicles so that fighters can be moved towards Afmadow.
Maj Chirchir said the Kenyan army's advance was going well, despite troops' progress being slowed down by muddy terrain and heavy rain.
Afmadow is about 90km north of the port city of Kismayo, al-Shabab's main economic power base.
Afmadow resident Hussein Osman Roble told Reuters news agency most people in the town had fled towards the Kenyan border.
"Jets have flown low over Afmadow, terrifying the residents, while al-Shabab is digging trenches and tunnels for defence inside and around Afmadow," he said.
The government controls very little territory, but does have several militant groups around the country it regards as allies, and it is backed by the international community.
Kenyan officials said they wanted to ensure al-Shabab militants were not able to operate anywhere near the two countries' shared border.
Nairobi has been infuriated by a string of abductions of foreign nationals near the border.
Most recently, two Spanish aid workers were seized from the Dadaab refugee camp.
A Frenchwoman living in Lamu and a British woman tourist have also been kidnapped in recent weeks and a British man killed.
After two decades of civil conflict, Somalia is awash with guns, and analysts say any number of groups could have carried out the kidnappings - including pirate gangs.
Our correspondent says the transitional government already relies on foreign troops from the African Union, so it is embarrassing to admit that it needs yet another country to intervene.
Previous foreign interventions in Somalia have ended in humiliating withdrawals - the US in 1992 and Ethiopia in 2009.
Correspondents say many Kenyans will fear their country could be bogged down in a long, unwinnable conflict.
Al-Shabab, which has links with al-Qaeda, has threatened Kenya on several occasions in the past.
But it has rarely acted outside Somalia - the only previous major attack it has said it carried out was a 2010 suicide bombing in Uganda's capital Kampala in which dozens of people died.
Nairobi Provincial Police commander Antony Kibuchi urged residents of the capital city be more vigilant following al-Shabab's warning on Monday.
"We have stepped up security across the city following these threats issued by al-Shabab," AFP news agency quotes him as saying.