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 wouldn'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 don'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 cannot 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, doesn'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.