This comes amid more violence in the highlands of Papua province, with two school teachers shot dead last week in Puncak district.
The West Papua Liberation Army claimed responsibility for at least one of the killings, saying the teacher was an Indonesian spy.
Indonesian military and police have evacuated a number of residents as they pursue the Liberation Army's guerilla fighters and supporters.
Thousands of villagers in this region have been displaced by violence between Indonesian security forces and the rebel group since it escalated two years ago.
Earlier this year, researchers said the vast majority of internally displaced people in West Papua originated from Nduga Regency where the armed conflict intensified two years ago.
About 8,000 of them have sought shelter in neighbouring Jayawijaya Regency.
Since then, according to solidarity groups, 400 displaced Papuans have died in Jayawijaya due to diseases and other strains.
The churches are urging the Office of the UN Commissioner for Human Rights to send a humanitarian team to Papua to investigate the condition of internally displaced people who are struggling to meet health, education and other basic needs.
They have also called for the Commissioner for Human Rights to visit Papua and carry out an investigation of human rights violations in Papua, as well as to monitor the thousands of military and police personnel deployed to Papua since August 2019.
In the past few years, the Commissioner repeatedly requested access to Papua, but Jakarta's expressions of willingness have yet to materialise in a visit, although the pandemic has been an added obstacle.
The West Papuan church leaders who signed the letter are Pastor Dorman Wandikbo of the Indonesian Evangelical Church, Reverend Benny Giay of the Kemah Injil Church, Rev. Andrikus Mofu, the Chairman of the Evangelical Christian Church, and Rev. Socratez Sofyan Yoman, the President of the Fellowship of Baptist Churches of West Papua.
Call for UN Council to look at Jakarta's Special Autonomy moves
The church leaders also called for serious attention from the UN Human Rights Council to moves by the Indonesian government to extend implementation of the 2001 Papua Special Autonomy Law which expires this year.
Many Papuans have voiced objections to Jakarta's plans for Special Autonomy Volume 2 with its aims of expanding civilian infrastructure, division of provinces and districts, and strengthening of security force bases in West Papua.
"The granting of Special Autonomy and the expansion of civilian and military infrastructure is a camouflage to hide the occupation of the Land of Papua for the benefit of exploiting natural resources," the church leaders said.
"To date 750,000 Melanesians have signed the Petition Against Special Autonomy for Papua Volume 2 and have demanded the right to self-determination."
The church leaders have condemned violence in Papua.
"We express our deep condolences over the shooting of two teachers in Beoga, Puncak Regency, Papua.
"At the same time, we are also concerned about the cooperation between the Papua Provincial Education Office and the Security Forces which allows the Army and Police to teach in civilian schools as part of the effort to label the Papuan National Liberation Resistance Organization (TPN / OPM) as terrorists."