All the six patients had mild symptoms and one of them has also recovered, the health minister said.
"Four new Omicron cases were detected, taking the total number of cases to six. Of the six cases, one patient has been discharged from the hospital. Currently, 35 Covid positive patients and 3 suspected cases are admitted to LNJP hospital,' said the health minister.
Delhi's first Omicron patient, a 37-year-old man, was discharged from the LNJP hospital, officials said on Tuesday.
The man, a resident of Ranchi, had travelled from Tanzania to Doha and from there, to Delhi on a Qatar Airways flight on December 2. He stayed in Johannesburg in South Africa for a week and had mild symptoms.
The LNJP hospital has been designated for treating patients infected with the new Omicron variant of Covid-19.
Meanwhile, another case Omicron, the fourth in the state, was recorded in Gujarat on Monday, taking India's toll to 41 cases.