Kenyan troops advanced towards a strategic rebel-held Somali town on Tuesday as heavy air strikes battered Shebab militant positions, army officials said.

"Our forces will be concentrating on operations in Afmadow region today, they started moving there late on Monday," said army spokesman Major Emmannuel Chirchir.

Kenyan troops have pushed at least 120 kilometres (75 miles) into Somalia to reach Afmadow region since Nairobi declared war on the Shebab militia and confirmed it had sent its army across the border on Sunday.

Guided by pro-government Somali forces, backed by heavy aerial bombardments but bogged down on mud tracks in heavy rain, Kenya has been hitting back against recent kidnappings inside Kenya blamed on the Islamists.

"So far everything is going on well," Chirchir added.

The assault has prompted dire warnings of revenge from the Shebab, who deny being behind recent kidnappings of foreigners from beach resorts and an overcrowded refugee camp.

The last time Somalia was invaded by one of its neighbours was in late 2006 when Ethiopia started an occupation that lasted two years and spurred the formation of the Al Qaeda-inspired Shebab insurgency.

"Kenya has peace, its cities have tall buildings and business is booming there, while Somalia is in chaos," Shebab spokesman Sheikh Ali Mohamud Rage said on Monday.

"If your government ignores our calls to stop its aggression on Somali soil, we will strike at the heart of your interests," he said, addressing the Kenyan population.

But Kenya said it was not frightened by the Shebab's grim warning.

"We will not give up at all, we will not be cowed or intimidated by the Shebab," Chirchir said.

It was unclear how long Kenyan troops planned to stay in Somalia but Nairobi had been under growing pressure to take action and attempt to restore confidence that it could safely host tourists and one of the world's largest aid communities.

Meanwhile in Kenya, police said they have stepped up security and beefed up their intelligence mechanisms, particularly in the capital Nairobi following the Shebab's threats of reprisals.

"I appeal to Nairobians and Kenyans in general to be extra alert and in case anybody sights any suspicious and strange person or any suspicious object to report to any police officer near him," Nairobi Provincial Police commander Antony Kibuchi said and circulated hotline numbers to the public.

"We have stepped up security across the city following these threats issued by Al Shabaab yesterday," he added.

AFP reporters did not see any signs of increased security in the capital, but did notice a higher-than-usual number of police checkpoints on the road leading into Nairobi from Dadaab, a sprawling series of camps in eastern Kenya that is home to 450,000 Somali refugees.