The reclusive dictator died of a heart attack or stroke on Saturday at the age of 69. The official Korea Central News Agency (KCNA) has called his third son, Kim Jong-un, the "great successor".
Steve Pearce, World Church Partnership Coordinator for the Methodist Church said in a statement: "The Methodist Church in Britain offers its prayers and support to its brothers and sisters in the whole of Korea today on the news of the death of Kim Jong-il.
"We pray especially for our partners the National Council of Churches in Korea and the Korean Methodist Church as they offer leadership at this difficult time.
"The Methodist Church echoes the concern expressed in the NCCK statement, reproduced below, that this time of sadness and anxiety should be the occasion of words and steps that build peace and reconciliation.
"The Church is encouraging people to pray for the nation at this difficult time."
It has issued a special prayer which asks that the people of North Korea will feel God's love "at this time of fear and uncertainty".
May our Christian solidarity with our sisters and brothers in Korea be a continuing and mutual source of strength," it reads.
In a separate statement, the National Council of Churches in Korea expressed its desire for peace.
"It should not be a moment which is threatening peace on the Korean peninsula and worsening of North and South relationship," it said.
"We hope that South Korean government take this [opportunity] to ease conflict between North and South.
"And we ask [the] international community to cooperate continuously, not taking this for [the] breaking of security on the Korean peninsula, but for building peace on the region of North East Asia."
Foreign Secretary William Hague said Kim Jong-il's death could be a "turning point" for North Korea.
"We hope that their new leadership will recognise that engagement with the international community offers the best prospect of improving the lives of ordinary North Korean people," he said.
"We encourage North Korea to work for peace and security in the region and take the steps necessary to allow the resumption of the Six Party Talks on denuclearisation of the Korean Peninsula."
While the international community speculates on North Korea's future under a new leader, reports that North Korea test fired a short-range missile this morning suggest there will be little change in the near future at least.
David Griffiths, South Asia Team Leader at Christian Solidarity Worldwide spoke of his desire to see a long-term interest in the country.
He tweeted: "I hope Kim Jong-il's death will occasion sustained international interest in the plight of North Korea's people, not just fear of insecurity."
The Methodist Church's Prayer for North Korea in full:
Creator God,
You love the people of this world with tenderness and care.
We pray that the people of the Korean peninsula may feel your love at this time of fear and uncertainty.
As we prepare to celebrate your coming among us as a vulnerable child, help us as we seek ways to tend the fragile flower of peace in your world.
May our Christian solidarity with our sisters and brothers in Korea be a continuing and mutual source of strength.
We pray in Jesus' name,
Amen.