The Hare Kṛṣṇa mantra is specifically mentioned in many Upaniṣads, such as the Kali-santaraṇa Upaniṣad, where it is said:
hare kṛṣṇa hare kṛṣṇa
kṛṣṇa kṛṣṇa hare hare
hare rāma hare rāma
rāma rāma hare hare
iti ṣoḍaśakaṁ nāmnāṁ
kali-kalmaṣa-nāśanaṁ
nātaḥ parataropāyaḥ
sarva-vedeṣu dṛśyate
"After searching through all the Vedic literature, one cannot find a method of religion more sublime for this age than the chanting of Hare Kṛṣṇa."
(Sri Caitanya Caritamrta-----1:3:40-----purport).

The Nārada-pañcarātra also praises the Hare Kṛṣṇa mahā-mantra as follows:
trayo vedāḥ ṣaḍ-aṅgāni chandāṁsi vividhāḥ surāḥ
sarvam aṣṭākṣarāntaḥ-sthaṁ yac cānyad api vāṅ-mayam
sarva-vedānta-sārārthaḥ saṁsārārṇava-tāraṇaḥ
"The essence of all Vedic knowledge—comprehending the three kinds of Vedic activity (karma-kāṇḍa, jñāna-kāṇḍa and upāsanā-kāṇḍa), the chandas, or Vedic hymns, and the processes for satisfying the demigods—is included in the eight syllables Hare Kṛṣṇa, Hare Kṛṣṇa. This is the reality of all Vedānta. The chanting of the holy name is the only means to cross the ocean of nescience." Similarly, the Kali-santaraṇa Upaniṣad states, "Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—these sixteen names composed of thirty-two syllables are the only means to counteract the evil effects of Kali-yuga. In all the Vedas it is seen that to cross the ocean of nescience there is no alternative to the chanting of the holy name."
(Sri Caitanya Caritamrta-----1:7:76-----purport).