Abdullah ibn Salam said: When the Messenger of Allah, peace and blessings be upon him, came to Medina, the people rushed towards him and it was said, “The Messenger of Allah has come!” I came along with the people to see him, and when I looked at the face of the Messenger of Allah, I realized that his face was not the face of a liar. The first thing he said was:

يَا أَيُّهَا النَّاسُ أَفْشُوا السَّلَامَ وَأَطْعِمُوا الطَّعَامَ وَصَلُّوا بِاللَّيْلِ وَالنَّاسُ نِيَامٌ تَدْخُلُوا الْجَنَّةَ بِسَلَامٍ

O people, spread peace, feed the hungry, and pray at night when people are sleeping and you will enter Paradise in peace.

Source: Sunan Ibn Majah 1334, Grade: Sahih
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Abdullah ibn Amr reported: The Messenger of Allah, peace and blessings be upon him, said:

اعْبُدُوا الرَّحْمَنَ وَأَفْشُوا السَّلَامَ

Worship the Most Merciful and spread peace.

Source: Sunan Ibn Majah 3694, Grade: Sahih
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Abdullah ibn Umar reported: A man asked the Messenger of Allah, peace and blessings be upon him, “Which Islam is best?” He said:

تُطْعِمُ الطَّعَامَ وَتَقْرَأُ السَّلاَمَ عَلَى مَنْ عَرَفْتَ وَمَنْ لَمْ تَعْرِفْ

To feed the hungry and to greet with peace those you know and those you do not know.

Source: Sahih Bukhari 28, Grade: Sahih

The meaning of spreading peace to “those you do not know” is to spread peace to the world in general.
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Allah said:

هَلْ أَتَاكَ حَدِيثُ ضَيْفِ إِبْرَاهِيمَ الْمُكْرَمِينَ إِذْ دَخَلُوا عَلَيْهِ فَقَالُوا سَلَامًا ۖ قَالَ سَلَامٌ قَوْمٌ مُّنكَرُونَ

Has there reached you the story of the honored guests of Abraham? When they entered upon him and said: We greet you with peace, so he answered: I greet you with peace, a people unknown.

Surah Adh-Dhariyat 51:24-25

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