Addressing thousands of Christians gathered in the Lake District, leading Bible expositor Ajith Fernando lamented that Christians were not "going out proactively in search of the lost".
He contended that 21st century Christians had become more concerned with their own comfort than they are with the needs of others.
"Whether you are in the East or the West, the North or the South, people are crying out for fulfilment," he said.
"We have the answer and what are we doing? Sleeping."
Fernando warned that there was a personal cost involved in finding the lost and that the church may need to consider changing its tactics to reach the unchurched.
"We are not going out pro-actively in search of the lost. To do that, we have to change.
"We may have to change our music, or our style of preaching. We may have to leave the confines of our church and go to where people are."
He continued: "Going to the lost is hard work. Sometimes we prefer to sleep in the comfort of our comfort.
"The world is headed for destruction, people have no hope without Christ, and we stay at home, satisfied with our methods, refusing to change, rejoicing that we are chosen. But perhaps it is better to call us frozen."
A second challenge came from Patrick Fung, of OMF, who urged Christians to have the same holy fear towards God as the early church.
He said that the fear of God would affect the way that Christians share their faith with others.
"Mission is not so much about doing something for God, as if we are doing God a favour," he said.
"Mission is about obedience, about acknowledging who God is, fearing God above everything else to serve His purposes.
"We are called to come before Him with a holy fear."
The Keswick convention runs until August 5 and is expected to draw around 15,000 people.