One abandoned bag was found at the military's Base Hospital in Naraina, a high-security area. The bomb squad was rushed there.
The army's bomb disposal squad used a sophisticated equipment called the real-time scanner to identify wire-like material within the bag.
Sniffer dogs were put in service too.
The bomb disposal squad placed cordtex around the bag and destroyed it.
Police sources later confirmed that no explosive material had been found in the bag.
Another bag was found lying on a motorcycle near the market in Greater Kailash-1, South Delhi.
The police used loudspeakers to ask the owner to meet them. He eventually showed up and claimed the package.
The man showed the contents of the bag to the police, who have taken him to a police station for further questioning.
Delhi has been on high alert since last week when two bombs exploded near-simultaneously in a crowded market in Hyderabad. 16 people were killed and more than 100 injured.
Nobody has been arrested yet for the terror attack in Hyderabad. The two bombs were tied to bicycles and placed near a cinema and a small roadside cafe.