Agni samskāra is an important part of tāntrikī prakriyā and derives inspiration from the Vedic yajna. But it would be incorrect to assume complete similarity. Most Indic spirituality can be described as Fire (Sun) based, as it is based on the awakening and upward ascent of the fiery Kuṇḍalinī, as opposed to the path of descent taught by a few rare schools (such as some Daoist ones).
For an advocate of Tantra śāstra, the agni or sacred fire is the generated by the union of śiva-śakti, Vāgīśvarī-Vāgīśvara, or Lakṣmī-Nārāyaṇa in the context of Pāncarātra. Some tantras ascribe kāma tattva to this mithuna to indicate the notion of sṛjana behind the janana of Agni:
Bhuvaneśvarī Saṃhitā states:
कामोन्मत्तं शिवं तत्र देवीमृतुमतीं तथा |
गणेशशैवशाक्तेषु ध्यायन् संपूजयेदिति ||
śāradātilaka:
वागीश्वरीमृतुस्नातां नीलेन्दीवरसन्निभाम् |
वागीश्वरेण संयुक्तामुपचारैः प्रपूजयेत् ||
Vāgīśvarī referred to here is not Sarasvatī but simply the Vāc aspect of Bhuvaneśvarī, as clarified by Gaṇeśavimarśinī :
शक्तिबीजेन वागीशीं वागीशं साध्यमन्त्रतः |
ततः शिवाय शक्त्यै च नमोऽन्तौ कथितौ मनू ||
वागीश्वरीमृतुस्नातां समस्ताभरणान्विताम् |
वागीश्वरेण संयुक्तां नमाम्यखिलसिद्धये ||
The Vaiṣṇava version of this concept is seen described as below:
लक्ष्मीमृतुमतीं तत्र प्रभोर्नारायणस्य च |
ग्राम्यधर्मेण संयुक्तमग्निं तत्र विचिन्तयेत् ||
Elsewhere:
वैष्णवे च तथा सौरे लक्ष्मीमृतुमतीं स्मरेत् |
नारायणस्य संयोगाज्जातमग्निं विचिन्तयेत् ||
Thus, the Agni here is of the form of consciousness (chit) and bliss (ānanda), arising from the union of Shakti and Shiva.
Specifically in the case of śrīvidyā, it is said in Jnānārṇava:
कामेश्वरीं कुण्डमध्ये सकामामृतसंयुताम् |
समावाह्य च संपूज्य तद्गर्भं वह्निमावहेत् ||
While the Agni is generated by well-known procedures (pāṣāṇabhava, śrotriyagehaja, etc.), the intent of the practitioner, as well as the mantra, are extremely important as these two aspects grant devatā svarūpa to Agni:
दीपाद्दीपान्तरन्यायात् स्फुरन्तं सर्वतोमुखम् |
श्वासमार्गेण मनुवित् कवचेन ततोऽर्चयेत् ||
For an aspirant of non-dual Tantra, abheda between upāsya and upāsaka is never forgotten; the practitioner embodies the ritualistic fire (which in the first place was generated by the fire of consciousness of the sādhaka and transferred to the external pit via breath) through nyasa of the seven “tongues” of Agni (Vahni is referred to as saptajihvā ) within the body of the upāsaka. The seven tongues of Agni have as their adhidevatās, deva, pitṝ, gandharva, yakṣa, nāga, piscāca, and rākṣasa.
These “tongues”, which represent specific shaktis of Agni, vary based on the purpose. For sāttvika purposes, one invokes hiraṇyā, kanakā, raktā, kṛṣṇā, suprabhā, bahurūpā and atiraktā. For rājasika purposes such as vashya etc., padmarāgā, suvarṇā, bhadralohitā, lohitā, śvetā, dhūminī and karālikā are invoked. In the case of tāmasika karmA such as māraṇa, one invokes viśvamūrti, sphuliṅginī, dhūmravarṇā, manojavā, lohitā, karālā and kālā.
An unusual dhyāna of agni is described in Rudrayāmala which is interesting for various reasons:
बन्धूकपुष्पसङ्काशं सुतप्तकनकप्रभम् |
पद्मस्थं यजमानार्थं वदनद्वयशोभितम् ||
सप्तच्छन्दोमयं देवं विमानोपरिसंस्थितम् |
त्रिधाग्रीवं त्रिपादाब्जं हव्यकव्यविनाशकम् ||
ब्रह्माध्वर्यूद्गातृहोतृचतुःशृङ्गविराजितम् |
पञ्चपात्रं पाशुपतं कापिलं च महामतम् ||
बौद्धं वैदिकमित्येतत् षट्+पिङ्गलविलोचनम् |
वेदार्थं च चतुःश्रोत्रं श्रौतशास्त्रमयध्वनिम् ||
सपातालजटाबद्धमौलिकोटीरभास्वरम् |
रक्ताम्भोरुहमध्यस्थं स्वस्तिकासनसंस्थितम् ||
पृष्ठदेशसमालम्बितार्त्तीयचरणाम्बुजम् |
सदा शब्दायमानं च राजमानं स्वतेजसा ||
शक्तिं वज्रं स्रुक्स्रुवौ च चतुर्भिर्दिक्षु बाहुभिः |
तोमरं तालवृन्तं च सौवर्णं घृतपात्रकम् |
वामैस्त्रिभिर्बाहुभिश्च दधानं रक्तवाससम् ||
bandhūkapuṣpasaṅkāśaṃ sutaptakanakaprabham |
padmasthaṃ yajamānārthaṃ vadanadvayaśobhitam ||
saptacchandomayaṃ devaṃ vimānoparisaṃsthitam |
tridhāgrīvaṃ tripādābjaṃ havyakavyavināśakam ||
brahmādhvaryūdgātṛhotṛcatuḥśṛṅgavirājitam |
pancapātraṃ pāśupataṃ kāpilaṃ ca mahāmatam ||
bauddhaṃ vaidikamityetat ṣaṭpiṅgalavilocanam |
vedārthaṃ ca catuḥśrotraṃ śrautaśāstramayadhvanim ||
sapātālajaṭābaddhamaulikoṭīrabhāsvaram |
raktāmbhoruhamadhyasthaṃ svastikāsanasaṃsthitam ||
pṛṣṭhadeśasamālambitārttīyacaraṇāmbujam |
sadā śabdāyamānaṃ ca rājamānaṃ svatejasā ||
śaktiṃ vajraṃ sruksruvau ca caturbhirdikṣu bāhubhiḥ |
tomaraṃ tālavṛntaṃ ca sauvarṇaṃ ghṛtapātrakam |
vāmaistribhirbāhubhiśca dadhānaṃ raktavāsasam ||