He came to the Prophet ﷺ, and Abu Bakr said, "Messenger of Allah, appoint him as leader over his people."Umar said, "Do not appoint him, Messenger of Allah."The two of them argued in the presence of the Prophet ﷺ until their voices grew loud.Abu Bakr said to Umar, "You only meant to oppose me."Umar replied, "I did not mean to oppose you."Then this verse was revealed, "O you who believe, do not raise your voices above the voice of the Prophet" [Hujurat 49:2].After that, whenever Umar bin Khattab spoke in the presence of the Prophet ﷺ, his words could not be heard until the Prophet asked him to repeat what he had said.The narrator added that Ibn Zubayr did not mention his grandfather, meaning Abu Bakr.
حدثنا محمد بن المثنى حدثنا مؤمل بن إسمعيل حدثنا نافع بن عمر بن جميل الجمحي حدثني ابن أبي مليكة قال حدثني عبد الله بن الزبير أن
قدم على النبي ﷺ فقال أبو بكر يا رسول الله استعمله على قومه فقال عمر لا تستعمله يا رسول الله فتكلما عند النبي ﷺ حتى ارتفعت أصواتهما فقال أبو بكر لعمر ما أردت إلا خلافي فقال ما أردت خلافك قال فنزلت هذه الآية {يا أيها الذين آمنوا لا ترفعوا أصواتكم فوق صوت النبي} قال فكان عمر بن الخطاب بعد ذلك إذا تكلم عند النبي ﷺ لم يسمع كلامه حتى يستفهمه قال وما ذكر ابن الزبير جده يعني أبا بكر
Bukhari also narrated it in "Holding Fast to the Book and the Sunnah," chapter on the dislike of excessive probing and disputation in knowledge, and extremism in religion and innovations, hadith no. 7302, from the hadith of Nafi bin Umar with the same chain.