"Somalia's government and its people will not allow forces entering its soil without prior agreement," Sharif Sheikh Ahmed told reporters in Mogadishu on Monday.
"There is only one thing we know about the Kenyan forces, and that is their offer of training to the national army of Somalia."
Kenya's unprecedented military incursion eight days ago stunned the region as its troops and tanks pushed some 100 kilometres (60 miles) into southern Somalia, areas controlled by the Al-Qaeda linked Shebab.
Sharif's statement appeared to contradict an agreement signed last week by Kenya and Somalia's defence ministers to "cooperate in undertaking security and military operations."
The agreement, inked in Mogadishu, limits Kenyan operations to Somalia's Lower Juba region.
"We have asked neighbouring countries to train our forces with the aim to participate in the liberation and peacemaking efforts that is going on in the country," said Sharif.
"But there are small issues we have discussed with Kenya which we see as unfair," he added, without elaborating.
Sharif's weak Western-backed government survives in Mogadishu under the protection of over 9,000 African Union troops, who have spent four years battling the Shebab's military drive to topple his administration.
His government controls only the war-ravaged capital, while the African Union Mission for Somalia (AMISOM) troops, from Uganda and Burundi, continue to fight bloody battles on Mogadishu's outskirts.
"AMISOM is in Somalia with an AU mandate and the consent of Somalia's government", Sharif said.
"There is collaboration with Kenya which is to assist Somalia's national army, so that our forces can fulfill their duties."
Kenya accuses the Shebab of attacks on its territory and a string of recent kidnappings of foreigners, charges the extremist militants reject.