Rabbi Shlomo Aviner was asked about the source of the statement of the Tikkun HaKlali and its value and said that there is no ancient source for this.
In the SMS message of the Olam Katan bulletin, Rabbi Aviner was asked: "Is there a higher value to the Tikkun HaKlali beyond the regular chapters of the Psalms?"
Rabbi Aviner replied: "There is no ancient source for this. But the regular chapters of the Psalms have the highest value of the highest. See Messilat Yesharim, chapter 20: "The majority of perseverance and study of the psalms of David and contemplation, helps to reach the degree of Hasidism, which is a supreme degree."
Rabbi Aviner clarified: "It is not permissible to be healed by the words of the Torah from the law of "Chover Chaver", but if one says the chapters of the Psalms in order to arouse one's soul to the fear of God and to purify one's soul, that right stands and protects it."