Sirisena, facing criticism over the failure to thwart the attacks, blamed the inspector general of police Pujith Jayasundara and defense secretary Hemesiri Fernando for not sharing advance warnings of the attacks with him.
Fernando resigned earlier in the week, but Jayasundara was holding on, the two officials said.
"He has refused to resign despite the president's request," one of the sources said. Under Sri Lanka's constitution, only parliament can remove the police chief through a lengthy process designed to shield officers from political interference.
The attacks in which more than 250 people were killed have exposed the divisions between Sirisena and Prime Minister Ranil Wickremesinghe, with both saying they had not seen warnings given by India's spy service about impending strikes on churches and the Indian embassy including one just hours before the attacks.
Jayasundara, the police chief, was handpicked for the job by Wickremesinghe. The first source at the president's office said Sirisena was still expecting him to turn in his papers. The second source confirmed the situation.
Both sources declined to be identified as they were not authorized to speak with media.
Jayasundara did not answer his phone or email seeking comments. An officer at the police department said the police chief had not resigned but did not come to work on Saturday.