NAIROBI, Kenya — Three weeks into their offensive against Somalia's Shabab Islamist militia, Kenyan forces are preparing for what's likely to be a decisive battle for the southern Somali port of Kismayo, which could either end Shabab's dominance in the region or add fuel to Somalia's decades-long civil war.

Even if the Kenyan military succeeds in capturing the port, its exit strategy is far from clear. Already, the Kenyan forces, which have never fought a war like this before, appear unexpectedly bogged down.

Kenya is pressing its attack on 10 Somali towns on the approaches to Kismayo. It's made clear that its aim is to seize the city, Somalia's main southern seaport and Shabab's most lucrative possession. The United Nations estimates that port revenues provide Shabab up to $50 million a year, or roughly half of its total funds.

On Monday, the Kenyan and Somali governments issued a joint appeal for international support in blockading Kismayo until Shabab's grip on the city is broken. But the role of other countries in the Kenyan offensive is unclear, though the United States believes Shabab is an al Qaida affiliate and that Somalia is a front line in the war on terror.

Kenya blames Shabab for a string of recent kidnappings targeting Western aid workers and tourists inside Kenyan territory. Shabab has denied responsibility but has threatened revenge attacks in Kenya's capital, Nairobi, East Africa's most important city. Last week, a Kenyan citizen confessed to being a member of Shabab and planning two grenade attacks on Oct. 24 in Nairobi. The youth, a Muslim convert from Kenya's rural western provinces, was promptly sentenced to life imprisonment.

With no roads in much of the Somali countryside, heavy rains have slowed Kenya's tank-equipped infantry to a near halt. That's left most of the offensive to Kenya's air force, the region's strongest, while Kenyan-trained Somali government troops and friendly militias have led the way on the ground.

Reached by phone, residents of Kismayo say that their city has been under steady aerial attack since the Kenyan offensive began Oct. 16. Abdirizak Ahmed, 31, said people are fleeing areas near the port and near Shabab encampments for fear of becoming collateral damage. But the rains have hampered them, too.

"With all this rain we cannot flee out of Kismayo, but we are adapting quickly to the situation by leaving areas close to Shabab," said Ahmed, who lives in the Hangash neighborhood near the Kismayo seaport.

To date, Shabab forces have avoided direct contact with the Kenyan troops, preferring instead to ambush Kenyan supply lines, a likely sign of the guerrilla tactics Kenyan forces would face if their invasion becomes a drawn-out affair.

But that's unlikely to be the case as the first major battle shapes up between the Kenyans and Shabab forces at Afmadow, an important trade hub about 50 miles north of Kismayo that the Kenyan military says it is preparing to capture and Shabab forces are congregating to defend.

Besides Afmadow and Kismayo, the Kenyan military also has targeted Burgavo, a corridor for fishing and charcoal trades, and has overrun Ras Kamboni, a port town near the Kenyan border that's considered a launching pad for the lucrative piracy trade.

According to residents reached by phone, the Shabab have called in hundreds of fighters from other regions of Somalia to counter the assault. Some of the Shabab reinforcements are believed to have been redeployed from Mogadishu, which the rebels largely abandoned in August.