Question
One mantra for praising all deities of three Lokas
Answer
There technically is "no only one mantra" if you're planning to please all the deities in the Triloka. But there are alternatives. If you wish to get the mantra which all the gods adhere to and pay allegiance, but non-Vedantic - then try the Gayatri Mantra. It is present in many sources, however I am taking it from the Surya Upanishad.
Surya Upanishad Verse 3
Aum bhūr-bhuva̱ḥ-suva̍ḥ |
tat sa̍vi̱tur vare̎ṇya̱m bhargo de'vasya dh'īmahi |
dhiyo̱ yo na̍ḥ praco̱dayā̎t ||Om, Earth, middle region and sky; we meditate on the adorable splendor of Savitar (Sun) who may inspire our thoughts.
Vishnu and Shiva mantras are generally favoured if you want direct blessings from every god out there.
Om Namo Bhagavate Vasudevaya.
Om Namo Bhagavate Rudraya.
These mantras are invoked at the beginning of many Puranas and stotras.
If you want an all encompassing Gayatri for deities combined in a single flow you can refer to Mahanarayana Upanishad and keep on chanting all the Gayatris.
Mahanarayana Upanishad
purushasya vidmahe sahasrakshasya mahadevasya dhimahi | tannorudrah pracodayat || 22||
tatpurushaya vidmahe mahadevaya dhimahi | tanno rudrah pracodayat || 23||
tatpurushaya vidmahe vakratundaya dhimahi | tanno dantih pracodayat || 24||
tatpurushaya vidmahe cakratundaya dhimahi | tanno nandih pracodayat || 25||
tatpurushaya vidmahe mahasenaya dhimahi | tannah shanmukhah pracodayat || 26||
tatpurushaya vidmahe suvarnapakshaya dhimahi | tanno garudah pracodayat || 27||
vedatmanaya vidmahe hiranyagarbhaya dhimahi | tanno brahma pracodayat || 28||
narayanaya vidmahe vasudevaya dhimahi | tanno vishnuh pracodayat || 29||
vajranakhaya vidmahe tikshnadam shtraya dhimahi | tannonarasim hah pracodayat || 30||
bhaskaraya vidmahe mahaddyutikaraya dhimahi | tanno adityyah pracodayat || 31||
vaishvanaraya vidmahe lalilaya dhimahi | tanno agnih pracodayat || 32||
katyayanaya vidmahe kanyakumari dhimahi | tanno durgih pracodayat || 33||
pathabhedahcaturmukhaya vidmahe kamandaludharaya dhimahi | tanno brahma pracodayat ||
adityaya vidmahe sahasrakiranaya dhimahi | tanno bhanuh pracodayat ||
pavakaya vidmahe saptajihvaya dhimahi | tanno vaishvanarah pracodayat ||
mahashulinyai vidmahe mahadurgayai dhimahi | tanno bhagavati pracodayat ||
subhagayai vidmahe kamalamalinyai dhimahi | tanno gauri pracodayat ||
navakulaya vidmahe vishadantaya dhimahi | tannah sarpah pracodayat ||
If you're looking for a deity-less all encompassing mantra, there is only ONE and ONE only:
AUM - ॐ
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