He was scheduled to make the presentation yesterday but the meeting was cancelled in view of Union minister Gopinath Munde's death.
The briefing is now expected to take place either this week or the early next week, Army officials said.
Soon after Modi became the Prime Minister on May 26, Gen Singh had met him for around 15 minutes and discussed the security scenario in the country.
During his detailed presentation before the Prime Minister, the Army chief is expected to give an overview of the situation along the borders with China and Pakistan, the militancy situation in Jammu and Kashmir and the northeast.
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The force is in dire need of artillery guns and is also scouting for new light choppers to maintain its troops and posts in the high altitude areas such as the Siachen glacier.
The procurement cases including acquisition of 145 Ultra-Light Howitzers, 197 light utility helicopters and several types of air defence weaponry are stuck due to one reason or the other.
The status of the new 17 Strike Corps being raised along the border with China is also likely to come up during the presentation to be given by the outgoing Army chief.