The security forces have widened their hunt from the village, about 160km from here, towards Kampung Tanjung Batu, some 2km from Kampung Tanduo yesterday.
The shootouts had reportedly occurred in three locations from 4.15pm.
Inspector-General of Police Tan Sri Ismail Omar said police and military personnel were moving into Kampung Tanjung Batu at about 3pm when the shootings occurred.
“We believe we have killed some of the enemy although we cannot confirm the number for now. There are civilians at Kampung Tanjung Batu,” he said, adding that no Malaysian security members were hurt.
Earlier, at 6.45am, security forces are believed to have shot dead a Sulu gunman at Tandau after they were fired upon in their mopping-up exercise.
Ismail said the police and military personnel had expanded their operational area following reports that some of the gunmen, who are said to be followers of the self-proclaimed Sulu Sultan Jamalul Kiram III, had slipped out of Kampung Tanduo and into Kampung Tanjung Batu.
Some 30 army trucks with soldiers as well as armoured personnel carriers and security vehicles were seen moving through Felda Sahabat yesterday before going to Kampung Tanjung Labian, which is located next to Kampung Tanjung Batu.
On claims by the Kiram family that the gunmen had taken four Malaysians two policemen, a soldier and a senior government officer as hostages, Ismail said: “I don't have that information.”
Armed Forces chief Jeneral Tan Sri Zulkifeli Mohd Zin, who was at the press conference, said the gunmen had moved to Kampung Tanjung Batu from Kampung Tanduo apparently for tactical reasons.
“They are very good at tactical deployment. We are searching for more weapons in our mopping-up operations in Kampung Tanduo. We believe some of the weapons have been buried,” he added.
Security forces had earlier seized a cache of weapons during the operation there.
Operation Daulat, which entered its second day yesterday, is to flush out the remnants of the Sulu armed group after Tuesday's aerial and artillery assault on Kg Tanduo.
But a number of the terrorists were believed to have slipped out of Kg Tanduo, with Tanjung Batu villagers reporting seeing up to 50 gunmen on Sunday night and a dozen or so the following night before the 7am bombings.
It is not known if their leader Raja Muda Azzimudie Kiram and his so-called royal Sulu army commanders were among those who entered Tg Batu, about an hour's walk away along the shore.
The joint police and military elite teams are believed to be moving towards some 100 houses within Kg Tg Batu and Kg Tg Labian from where families have fled on hearing about the arrival of Sulu gunmen on Sunday night.
It is believed that some 15 gunmen or so could be hiding in Kg Tg Batu with families who are unable to leave the area which has been declared a Red Zone.
The fate of Azzimudie remains unclear as the Kiram family in Manila keeps claiming that they were still in contact with him while some villagers claimed yesterday that they heard that he got out of Tanduo some time ago.
According to the official count, nine bodies of Sulu gunmen had been recovered, but sources claimed that some 50 bodies of the estimated 130 gunmen were scattered around in Tanduo.