The superscription to Psalm 53 says, "To the choir director: according to mahalath. A Maschil of David." Concerning "mahalath," the meaning of the Hebrew is obscure. It may refer to a kind of sad melody. This psalm of instruction refers to a time when David was being attacked by the Gentiles.
In verses 1 through 5 we are told that none among all the sons of men was doing good. Here David is saying that none among the Gentiles is doing good. This psalm puts all the Gentiles into a "ditch" and uplifts the Jews to heaven.
Verse 1 says, "The fool has said in his heart,/There is no God./They are corrupt and do abominable deeds;/There is none who does good." This verse refers not to Jews but to Gentiles, and the fool here is a Gentile. Paul quoted this verse, along with verses 2 and 3 in Romans 3:10-12, referring to all men.
In verse 4 David goes on to say, "Have they no knowledge, all who do iniquity,/Who devour my people as they would devour bread/And do not call upon God?" Here David seems to be saying that this is God's word to the Gentiles.
In verse 6 we see that the psalmist wanted to enjoy God in His salvation from His house when God turned the captivity of His people. This verse says, "Oh that the salvation of Israel might come forth from Zion!/When God turns the captivity of His people,/Jacob will exult, Israel will rejoice." The salvation here is only for the Jews.