Lord Sri Krishna decided against using weapons in the battlefield. It was his decision keeping in line with a Divine Plan(which was known only to Lord Sri Krishna).
This "divine plan" was the very cause of the Mahabharata War—and the aim of the plan was "to cleanse all Kshatriyas with weapons and send them to Swarga". This is explained clearly in the Mahabharata (Book 12, Shanti Parva, Section II),
Narada said, 'It is even so, O mighty armed one, as thou sayest, O Bharata! Nothing could resist Karna and Arjuna in battle. This, O sinless one, that I am about to tell thee is unknown to the very gods. Listen to me, O mighty-armed one, as it befell in former days. How all the Kshatriyas, cleansed by weapons should attain to regions of bliss, was the question'
I have the question that why he(Lord Sri Krishna) does not participate directly in the war
Lord Sri Krishna did not participate directly in the war because of the divine plan explained above.Wars, infact, originate in the "hearts and minds" of people.The outwardly manifestation of the "war within" was the deadly Mahabharata War, which left few survivors—the Pandava brothers, Ashwattama, and a few others.
The Srimad Bhagavad Gita,it is believed, - can accelerate the process of inner transformation—transformation of hearts and minds.
He never supported the Kauravas even after Duryodhana asked first for him instead of Narayani Sena.
With regard to the above statement in the Q - It was Arjuna who was given the privilege of asking first.Duryodhana was petrified that Arjuna would ask for the mighty Narayani Sena.But...Arjuna did not do that.Arjuna asked for Sri Krishna.
Reference-The Mahabharata Book 12:Santi Parva,Rajadharmanusasana Parva