In the Brihad-Vishnu-Sahasranam-Stotra in the Uttara-khanda of the Padma Purana (72.335) we find the following words that were spoken by Lord Shiva to his wife, Durga Devi:

rama rameti rameti
rame rame manorame
sahasra-namabhis tulyam
rama-nama varanane

“O Varanana, I chant the holy name of Rama, Rama, Rama and thus enjoy this beautiful sound. This holy name of Ramacandra is equal to one thousand holy names of Lord Vishnu.”

In the Laghu-bhagavamrita (1.5.354) by Srila Rupa Goswami we find the following verse quoted from the Brahmanda Purana:

sahasra-namnam punyanam
trir-avrttya tu yat phalam
ekavrttya tu krsnasya
namaikam tat prayacchati

“The pious results derived from chanting the thousand holy names of Vishnu three times can be attained by only one utterance of the holy name of Krishna.”