Allah, exalted be His praise, says: "And We sent down from the sky pure (purifying) water." [Surah al-Furqan: 48]
And He said: "Then if you do not find water, perform tayammum with clean earth." [Surah al-Nisa: 43]
Abu Abdullah Muhammad bin Idris al-Shafi'i (may Allah be pleased with him) said: "The apparent meaning of the Qur'an indicates that all water is pure, whether it is sea water or other than it, and a hadith has been narrated from the Prophet (peace and blessings be upon him) on this matter which agrees with the apparent meaning of the Qur'an; (however,) in its chain there is a narrator whom I do not know." Then he mentioned the hadith that follows.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / Q1
Sayyiduna al-Mughirah bin Abi Burdah heard Sayyiduna Abu Hurayrah (may Allah be pleased with him) say that a man asked the Messenger of Allah (peace and blessings be upon him): O Messenger of Allah! We travel by sea and take a small amount of water with us; if we perform ablution with it, we will remain thirsty. May we perform ablution with sea water? The Messenger of Allah (peace and blessings be upon him) said: "Yes, its water is pure and its dead (animals) are lawful."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 1
Sayyiduna al-Mughirah bin Abi Burdah (may Allah have mercy on him) heard Sayyiduna Abu Hurayrah (may Allah be pleased with him) say: One day we were with the Messenger of Allah (peace and blessings be upon him) when a fisherman came and said: "O Messenger of Allah! We travel on the sea for the purpose of fishing, and one of us takes a water vessel with him, hoping that he will catch fish close by. Often that is how it happens, but sometimes he does not find any fish until he reaches such-and-such a place in the sea, which he had not expected to reach. Sometimes he has a wet dream, or his ablution is broken; then if he takes a ritual bath (ghusl) or performs ablution with this water, perhaps thirst will destroy one of us. What is your ruling about sea water? May we take a ritual bath or perform ablution with it when we fear this?" The Messenger of Allah (peace and blessings be upon him) said: "Take a ritual bath and perform ablution with its water, for its water is pure and its dead (animals) are lawful."
This same hadith is narrated from the Prophet (peace and blessings be upon him) by Sayyiduna Ali bin Abi Talib (may Allah be pleased with him), Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) and Sayyiduna Abdullah bin Amr (may Allah be pleased with them both).
The narrator whom al-Shafi'i meant by his words "in its chain there is someone I do not know" is Salamah bin Sa'id (as some named Sa'id bin Salamah), or al-Mughirah, or both of them; however, the one who established its chain is thiqah (trustworthy): Malik bin Anas placed it in the Muwatta, and Abu Dawud recorded it in the Sunan.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 2
Imam al-Shafi'i (may Allah have mercy on him) said: Abd al-Aziz bin Umar narrated, through Sa'id bin Thawban and Abu Hind al-Firasi, from Sayyiduna Abu Hurayrah (may Allah be pleased with him), that the Prophet (peace and blessings be upon him) said: "Whoever is not purified by the (water of the) sea, may Allah Almighty not purify him."
Ibrahim bin al-Mukhtar said: Abd al-Aziz bin Umar narrated a hadith like it, but he did not mention the name al-Firasi.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 3
Amir bin Wathilah (may Allah be pleased with him) said that Abu Bakr al-Siddiq (may Allah be pleased with him) was asked about the dead (animals) of the sea, and he said: "Its water is pure and its dead (animals) are lawful."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الطهارة / 4