"I believe it's the first importance that we keep that solidarity, friendship and presence," he added, according to the UAE-based National news agency.
Williams, who is regarded as "first among equals" within the 77 million-large Anglican Communion, is currently making his way through the Holy Land with plans to meet with Christians in Jordan, Israel, and Palestine.
The archbishop will also meet with local heads of state and government and lead an Anglican delegation in a fourth round of discussions with the Chief Rabbinate of Israel. He will be accompanied throughout the trip by Anglican Bishop in Jerusalem Suheil Dawani and Church of Ireland Bishop Michael Jackson of Clogher, the Anglican chair to the Anglican Jewish Commission.
On Saturday, the Anglican leader laid the cornerstone for a new church on the eastern bank of the Jordan river and reiterated his remarks on the Middle East's dwindling Christian population, saying that the departure of Christians from the region "represents a source of extreme concern for us."
But amid the turmoil and escalating violence, Williams urged the some 600 Jordanian Anglicans to not lose hope.
"It's the same world as the one into which Jesus came – in so many ways a place that can drive us to despair or rage, and yet now and forever a world in which God is real, so that neither rage and despair can be the only or the ultimate option for us," he said, according to the National.
"May the God who has called us his beloved sons and daughters in baptism give us the courage to be faithful to this gift of presence – the courage always to begin again, day after day, to be a Christian."
Christians currently make up between 1.5 to five percent of Jordan's six million people. In 1950, Christians made up about 30 percent of the Jordanian population. The drop has been largely attributed to the higher birth rates of Muslims in the region as well as the influx of Muslim immigrants from neighboring countries.
Also contributing to the shrinking figure is the loss of many Christians who move to Europe, the United States and Canada for better opportunities.
Although relations between Muslims and Christians are generally good in Jordan, the U.S. State Department has noted that the government's application of Shari'a (Islamic law) infringes upon the religious rights and freedoms laid out in the Constitution by prohibiting conversion from Islam and discriminating against religious minorities in some matters relating to family law, including inheritance practices.
Members of unrecognized religious groups – such as the Baptist Church, the Free Evangelical Church, the Nazarene Church, the Assemblies of God, and Christian and Missionary Alliance – also face legal discrimination.
Notably, however, the State Department last year praised Jordan, among other countries, for its promotion of interfaith dialogue efforts.
"International interfaith initiatives are growing in many parts of the world, and the Middle East region in particular has seen a growing interest in intra-faith and interfaith dialogue," the department noted.
Among the efforts noted was Jordanian King Abdullah's "Amman Message" of 2004, which the State Department acknowledged for its promotion of a number of interfaith conferences and activities, and for having been an "important precursor" to further efforts.