Armed Forces Chief of Staff General Eduardo Ano said Abu Rami was "a very notorious Abu Sayyaf leader", who had climbed the ranks of separatist group.
The military chief said Askali had led a group of militants who traveled by speedboats to Bohol province in an apparent bid to carry out a kidnapping in the region, which is popular for its beach resorts and wildlife.
The Philippine military chief says troops have killed a key Abu Sayyaf commander who had been blamed for the beheadings of two Canadians and a German hostage and was with militants who clashed with government forces on a central resort island.
The US and Australian governments later warned their citizens about possible "terrorist" abductions in Bohol and Cebu.
The military spokesman said the goal was to kill or capture by Wednesday the remaining infiltrators and contain the fighting outside the town of Inabanga, about 80 kilometres (50 miles) from the tourist section of Bohol.
Helicopter gunships were used to bomb the militants, who fought back with high-end sniper rifles while holed up in a concrete house, according to officials.
"They are all running for their lives", he said. The claim could not be independently confirmed.
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Ano said Abu Rahmi's group also attacked a German couple on a yacht at sea past year, murdering the woman on board and taking the man hostage.
Authorities in Cebu, an island of almost five million people, warned their citizens about potential kidnapping raids following the Bohol attack.
"They are on the run".
As the government moved to contain the fallout on tourism, Ano said the military would repel similar incursions.
He did not specify how many security forces had been drafted in but said that they were from the army, navy and air force.
Ano said Rami and 10 of his men allegedly traveled to Bohol to abduct foreign and local tourists but their plans were foiled when residents reported the presence of armed men to authorities. Hoteliers and visitors told AFP the incident had not affected tourist traffic on the island, though there was increased police security.
"Yes, Abu Rahmi is among those Abu Sayyaf killed in Bohol operation, six killed among the enemies, our troops recovered another body on the site of encounter", he added.
Philippine President Rodrigo Duterte has ordered troops to destroy the extremists and has threatened to declare martial law in the country's south if the threat posed by the Abu Sayyaf and other extremist groups aligned with the Islamic State group gets out of control.