When a person can think about universal peace then that person has risen above ignorance. Peace in universe is connected to our inner soul. There is only one single mantra for Universe and Universal Peace. It is the Shiva Panchakshari Mantra.
Mantra - ॐ
नम: शिवाय
Om Namah Shivaya
Om Namah Shivaya
The entire cycle of creation is hidden in this mantra. Om is the primordial sound. It carries in it creation, sustenance and transformation. There is nothing beyond it. And who performs all these functions Shiva. Who is Shiva? Only Shiva is there. That is the combination of Purusha and Prakriti. It is the combination of the male and female.
Keep chanting the mantra whenever possible and you will find inner peace and this will reflect as universal peace.