In an Easter message, David Cameron said values which the country treasured included responsibility, hard work, charity and compassion.
These were Christian values that "speak to everyone in Britain, to people of every faith and none", he said.
The ideology behind attacks such as Brussels could be defeated by "standing up proudly" for those values, he said.
"Values of responsibility, hard work, charity, compassion and pride in working for the common good and honouring the social obligations we have to one another, to our families and to our communities - these are values we treasure," he said.
"They are Christian values and they should give us the confidence to say 'Yes, we are a Christian country and we are proud of it'.
"But they are also values that speak to everyone in Britain - to people of every faith and none.
"And we must all stand together and defend them."
He added: "When terrorists try to destroy our way of life as they have tried to do again so despicably in Brussels this week - we must stand together and show that we will never be cowed by terror.
"We must defeat the pernicious ideology that is the root cause of this terrorism by standing up proudly for our values and our way of life."
The prime minister has faced criticism in the past from secularists and some other public figures for describing Britain as a Christian country.
He has previously described himself as a "committed" but only "vaguely practising" Christian, who is "full of doubts" on big theological questions.
In other comments, Mr Cameron said Easter was a message of hope and praised the work done by faith and voluntary organisations.
"We see that hope every day in the many faith-inspired projects that help the homeless, that get people into work, that help keep families together and offer loving homes to children who need them," he said.
"We see it in the compassion of church leaders and volunteers who visit our hospitals, care homes and hospices - and those who comfort the bereaved.
"And we see that hope in the aid workers and volunteers who so often risk their own lives to save the lives of others in war-torn regions across the world."
Britain should be proud of being a "Christian country with Christian values", the prime minister has said.