Lawyers supporting the American also said there was "no evidence" to support accusations that he belonged to a terrorist organisation Turkey blames for a failed coup.
In a statement to the international body's Human Rights Council representatives from the European Centre for Law and Justice (ECLJ) said: "The UN has long stood to protect the human rights of all people.
"In intervening on behalf of Pastor Brunson, the UN will once again demonstrate its commitment to ensuring that freedom of religion exists for all people, regardless of their faith."
Mr Brunson was summoned to a local police station in October 2016 and later charged with links to a failed plot to overthrow the Turkish government in July 2016.
Supporters claim he is effectively a political prisoner being held as a bargaining chip by Turkey as it seeks the extradition of preacher Fethullah Gülen, which it blames for the doomed action.
Brunson, who has led a small Protestant church in the coastal city of Izmir for 23 years, has been told he faces up to 35 years in prison.
The statement goes on to say: "The indictment against Pastor Brunson was 62 pages long, wholly lacking in merit, and provided no evidence regarding criminal action against Pastor Brunson, but was rather replete with hearsay from secret witnesses."
The ECLJ also urges Turkey to uphold its obligations under the International Covenant on Civil and Political Rights and the Universal Declaration of Human Rights in its handling of Andrew Brunson.
Their statement continues: "The ECLJ... further requests that the UN continue to make every effort to ensure that Pastor Brunson is not only treated with great care, but that he is released and allowed to return home to the United States without injury or delay."
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