The Prophet (ﷺ) did Ramal in (first) three rounds (of Tawaf), and walked in the remaining four, in Hajj and Umra.
Sahih al-Bukhari Book 25, Hadith 90
← Previous Hadith I saw Allah's Messenger (ﷺ) arriving at Mecca; he kissed the Black Stone Corner first while doing Tawaf and did ramal in the first three rounds of the seven rounds (of Tawaf).

Sahih al-Bukhari Book 25, Hadith 89 Next Hadith → "`Umar bin Al-Khattab addressed the Corner (Black Stone) saying, 'By Allah! I know that you are a stone and can neither benefit nor harm. Had I not seen the Prophet (ﷺ) touching (and kissing) you, I would never have touched (and kissed) you.' Then he kissed it and said, 'There is no reason for us to do Ramal (in Tawaf) except that we wanted to show off before the pagans, and now Allah has destroyed them.' `Umar added, '(Nevertheless), the Prophet (ﷺ) did that and we do not want to leave it (i.e. Ramal).'

Sahih al-Bukhari Book 25, Hadith 91