Their visit comes months after the Iraqi Christian community experienced one of its worst ever attacks, when militants opened fire on the congregation of Our Lady of Salvation in Baghdad last October, killing dozens.
Archbishop Dr Avak Asadourian, Primate of the Diocese of Iraq in the Armenian Orthodox Church, summed up the reality facing the Iraqi church.
"We have parishes that have completely gone, and all churches have experienced decline in the number of worshipers," he said.
"If this continues for some time I am afraid our churches will be in peril."
Despite the pressures, the church is still active in the community, providing food and lodging for people suffering from economic hardship.
"The need is very sharp and whatever we give them is not enough sometimes," he admitted.
Archbishop Mar Georgis Sliwa, Metropolitan of the Iraq Diocese of the Holy Apostolic Catholic Assyrian Church of the East, said the most urgent need for Christians in Iraq was security and the empowerment of the state in securing the rights of all citizens regardless of their religion or ethnicity.
The Archbishop shared his desire to see a return to "normal life" in the country, and the day when the state would be in the position to develop the nation and provide investment.
While he spoke of his hope for the thousands of Iraqi Christians who have left Iraq to one day return, he added that "the urgency now is for those who still live in Iraq".
"The only hope is to bring back hope," he said. "Despite the difficulties we are still hopeful because we are Christians and we love our country."
The Christian population in Iraq has declined dramatically since the US-led invasion in 2003 from around 1.2 million to an estimated 400,000 to 600,000 today. Since then, Islamic militants have deliberately targeted Christians – seen as an ally of the West - with a view to eradicating them from the country.
The attacks have triggered a refugee crisis, with a recent report from the International Organisation for Migration estimating that at least 1,000 Christian families have fled to Kurdistan, with around two thirds of them making the move in the last two months alone.
Others have, along with 1.5 million of their fellow Iraqis, sought refuge in Syria, Jordan, Lebanon and western countries.
WCC General Secretary the Rev Dr Olav Fykse Tveit, said: "Christians in Iraq represent one of the most ancient and durable communities in the world.
"Along with all Iraqis they are being severely stressed and threatened in present circumstances, so we are anxious to express our ecumenical solidarity with the women and men there and to work with churches and others to address their plight."