Jalaluddin said Zakiah is reported to be safe and unharmed and the abductors have given him space to contact his wife and children.
"About 42 calls have been made, with most of the calls made in the evening and afternoons," he said, adding that police have monitored each call.
He said according to Zakiah, they were constantly moving from one location to another to avoid getting tracked down by the Philippine authorities.
"The negotiation process takes time due to the high price set by the abductors," he said without revealing the amount demanded. However, it is believed to be RM5 million.
On July 12, 32-year-old Corporal Ab Rajah Jamuan was shot dead while 26-year-old Zakiah was abducted by eight gunmen who ambushed the Smart Water Bungalow Resort jetty in Mabul Island.
On another note, he said there have been several arrests during the extended 12-hour curfew imposed in the six districts in the East Coast. However, he did not state any figure.
Meanwhile, Jalaluddin said the State Criminal Investigation Department is a force to be reckoned with but there is still room for improvement.
He said the mission and vision of the Royal Malaysian Police can be achieved with cooperation, hard work and full commitment from all quarters particularly in conducting duties.
"We must be aware that the community depends on us to keep the peace and security and when crime as well as drug related social ills continue to rise, it would mean that we have failed in the eyes of the community," he said, adding that efforts should be take to initiate improvement.
Jalaluddin gave the advise after witnessing the handing over of duties to new State Criminal Investigation Department Chief SAC Salehhudin Abdul Rahman and State Deputy Criminal Investigation Chief ACP Jauteh Dikun at the police headquarters in Kepayan, Monday.
He expressed confidence in the capabilities and expertise of the two newly appointed officers.
"I believe their appointment will further strengthen the Sabah police contingent, particularly the Criminal Investigation Department, as both are experienced and fully committed," he said.
Former Acting State Criminal Investigation Department Chief SAC Mohd Shariff Abd Wahid, who was deputy CID chief until the transfer of former CID chief SAC Omar Mammah to Bukit Aman, recently, handed over duties to both Salehhudin and Jauteh during the ceremony.
Shariff who has served in Sabah for six years will be promoted to the Kedah Police Contingent where he will take over the post as Crime Prevention and Community Security Department Chief.
Meanwhile, Salehhudin from Melaka, pledged to continue the duties started by the former State CID Chief.
"We will look into the areas to be improved and strengthened," he said, adding that he will discuss with the State Police Commissioner prior to visiting other districts in the State.
"We will work together, complement each other and ensure the mission and vision of the police force will be achieved," he said.