The petitioner through his counsel C B Pandey has alleged that a new kind of communalism was being spread in the name of love jihad.
He has sought direction to restrain use of the word Love Jihad and action against Adityanath.
The petitioner has also sought direction to restrain Union minister Mishra from campaigning during by-election for Vidhan Sabha and Lok Sabha.
He has sought direction that a high-power committee should be constituted to issue directives to check communal violence.
On the request of the state government counsel and the EC counsel, the court granted 10 days time to seek instructions.
The court has fixed September 15 as the next date of hearing.
Adityanath has alleged that Love Jihad, a term coined by Hindutva activists to protest alleged organised conversion of Hindu girls, is an "international conspiracy" against India.
The firebrand leader has come under attack from Congress and other parties for his controversial comments against the minorities.