Nairobi , Kenya ( CNN ) -- Conflicting accounts emerged Thursday over whether the extremist group Al-Shabaab has signaled a desire to negotiate with Kenya amid a Kenyan military offensive targeting the group . `` They want to talk , '' said a Kenyan official who did not want to be named because he is not authorized to talk to the media . A spokesman for the Kenyan government , however , disputed that account and said Kenya would n't talk with Al-Shabaab even if the group did want to negotiate . `` Al-Shabaab has not contacted Kenya in any way , '' said the spokesman , Alfred Mutua . `` There are no plans whatsoever for Kenya to negotiate with Al-Shabaab . Kenya does not negotiate with outlawed groups . '' He said Kenyan troops have enjoyed success since crossing the border into Somalia to pursue Al-Shabaab , which the United States and several Western nations view as a terrorist organization . `` They are running scared . I think they are busy running for their lives , '' Mutua said . `` They do n't have time to talk . '' Kenyan troops struck several Al-Shabaab training sites in Somalia early Thursday , a military spokesman said . The militant group , which includes many rival factions with different leaders , operates from Somalia . The group 's leaders were said to be reaching out for possible negotiations two weeks after Kenyan troops stormed into Somalia to hunt for Al-Shabaab , which Kenya blames for recent kidnappings of foreigners in the nation . But Sheikh Mukhtar Robow Ali , Al-Shabaab 's second-in-command who is also known as Abu Mansur , told supporters protesting in Mogadishu against the Kenyan incursion that if Kenya struck targets in Somalia , the militant group would strike back . Kenya has said its forces aim to take the Somali port city of Kismayo , described by the United Nations as a key stronghold and source of cash for Al-Shabaab . The United Nations estimates the group collects up to $ 50 million a year from businesses in Kismayo , about half of its annual income . Robow urged what he said were Al-Shabaab-trained fighters in Kenya to take action in return , with the Kenyan port of Mombasa a target . ''Carry out attacks with heavy losses on Kenya , '' Robow said . `` If Kenya closes the sea port in Kismayo , attack its banks , its port , its foreign guests and wherever there is a high-value target . '' Kenyan officials have declared self-defense justifies crossing the border with Somalia , saying a recent spate of abductions threatened its security and constituted an attack . Kidnappers have seized two aid workers and two European tourists in the past month . `` We have looked at what is going on ... and decided that unless we move in now , Al-Shabaab is not diminishing , it is becoming bigger and bigger , '' Mutua said . The war on terror can not be won without dismantling the group 's power , he said . Efforts to flush out the terror group will take a `` couple of months , if that , '' Mutua said , adding that `` weeks '' would be a more ideal time frame . Analysts and diplomats have raised concerns over the incursion , saying it gives the terror group a reason to strike Kenya . `` If there is anything we have learned in the last couple of decades is that foreign intervention , especially military intervention , does n't work in Somalia , '' said Rashid Abdi , an analyst for International Crisis Group . `` I definitely understand Kenya 's anxiety about the terror threat emanating from Somalia ... but I think there is more that Kenya could have done inside the country . '' While noting Kenya 's `` right to defend itself , '' the U.S. Embassy in Nairobi said it was not part of the decision to send troops to Somalia . `` The United States did not encourage the Kenyan government to act nor did Kenya seek our views , '' said Katya Thomas , the embassy 's press officer . `` We note that Kenya has a right to defend itself against threats to its security and its citizens . '' Somali President Sharif Ahmed thanked Kenya on Wednesday for helping battle the extremist group two days after he accused the nation of overstepping its boundaries . Journalist Mohamed Amiin Adow contributed to this report .
NEW : An Al - Shabaab commander says its militants will strike Kenyan targets in return . A Kenyan government official denies Al - Qaeda overture . Another Kenyan official said Al - Shabaab wants to talk . Kenyan troops entered Somalia two years ago to pursue Al - Shabaab .