* Al Qaeda-linked rebels extend deadline for officials
* Shabaab have demanded Kenya frees Muslim prisoners
* Nairobi says will negotiate with "terrorists"
* KDF says trying to confirm Shabaab claim of execution (Recasts with Kenyan reaction)
By Feisal Omar
MOGADISHU, Feb 15 (Reuters) - Kenyan defence officials said on Friday they would not negotiate with Somali militants linked to al Qaeda who said they executed a Kenyan army private at midnight on Thursday.
The al Shabaab militants, who want to impose a strict version of sharia, or Islamic law, said they killed the soldier after the expiry of an ultimatum for the release of Muslims held by Kenya on terror charges.
The rebels also postponed the execution deadline by 72 hours for five other hostages, including two government workers.
Colonel Cyrus Oguna, spokesman for the Kenyan military which has been battling al Shabaab in Somalia since October 2011, confirmed the soldier was one of its troops, but said the Kenya Defence Forces was investigating the claim of the execution.
He said the soldier had been abducted and was not captured during the KDF's operations in Somalia.
Oguna also ruled out negotiations with the rebels.
The Kenyan defence forces have always said none of its soldiers was believed held as prisoners of war by al Shabaab.
Nairobi sent its troops across the border to pursue the rebels after the insurgents kidnapped Western tourists and Kenyan security forces on Kenyan soil.
"The soldier was abducted long before the KDF crossed into Somalia," he said in Kenya's capital Nairobi.
"The government position has been clear, and it will not change. At no time will we negotiate with terrorists."
Oguna said the Kenyan military were putting pressure on the insurgents, and were hopeful of over-running them and rescuing the detained captives.
"Our effort in Somalia is getting closer to the terrorists to ensure they are rescued or released. As al Shabaab continues to lose ground, there is the likelihood of them releasing their captives so they can run away," Oguna said.
The insurgents on Jan. 23 had given Kenya a three-week deadline to free its fighters held by the east African country, but Kenya said it would not meet the demand.
Prior to the ultimatum, the group had killed French hostage Denis Allex to avenge France's persecution of Muslims and its military operations against Islamists, including in Mali.
FRESH 72-HOUR DEADLINE
Security analysts describe al Shabaab as a declining force that no longer controls much territory in Somalia and is not a threat to the Somali government or African Union forces there, but is still capable of mounting sporadic attacks.
The rebels said in a statement there was still a chance of securing the release of the five prisoners, and gave the name of the soldier they claim to have executed.
The rebels said they would give more time to the remaining hostages in response to their families' pleas.
The two government workers are Mule Yesse Edward, a local administrator, and Fredrick Irungu, who worked for the Kenyan ministry of immigration. Both were captured in January last year when the militants crossed the border into Kenya and attacked a police post in Wajir county, killing several police officers.
"In 72 hours, the prisoners will either lose their lives because of their government's betrayal or celebrate their government's assistance and rejoice in their freedom," the militants said.
Kenya holds several suspects for alleged links with al Shabaab and extradited others to Uganda suspected of involvement in a deadly 2010 suicide bombing in Kampala, claimed by al Shabaab, that killed 76 people. (Additional reporting from Nairobi and writing by James Macharia; Editing by Michael Roddy)