Delhi Police said Wednesday that Major Nikhil Handa — who is accused of murdering a fellow officer's wife — has been giving them "misleading information day after day".
But they added that they have "done 90% of the work" and were close to cracking the case.
"Accused Nikhil Handa is giving us misleading information day after day. We have done 90% of the work and in coming days the truth will come out," DCP, West Delhi Vijay Kumar said.
News reports meanwhile quoted police as saying the first person Handa had called after allegedly murdering Shailaja Dwivedi was a woman friend he had met on a dating site.
Handa was on Monday remanded in police custody for four days.
Police said Wednesday that they had not yet found the weapon used to kill Shailaja.
Shailaja had been found dead with her throat slit in Delhi's cantonment area on June 23. Police said her killer had repeatedly run over with a car to try and mask the crime.
News reports later said Handa had been obsessed with Shailaja — that he had made 3,000 calls to her in one year — and had been trying to convince her to leave her husband and marry him.
Handa is married himself.