Pope Benedict XVI praised the UK as a "force for good" today as thousands of people turned out to greet him on the first day of his historic visit.
But he also delivered a warning about "aggressive forms of secularism", urging the nation not to lose its traditional values as it "strives to be a modern and multicultural society".
The first state visit to the UK by a pope came amid renewed anger at the worldwide child abuse scandal that has engulfed the Roman Catholic Church and dogged the Pope's own religious career.
As he flew to Scotland, the Pope spoke of his "sadness" over his church's handling of child abuse scandals.
He said abusive priests had not been dealt with decisively or quickly enough.
The Pope's comments, to reporters on board his plane, marked his most thorough admission to date of failings in the way the sex abuse scandal was handled.
But despite the controversy, his followers turned out in large numbers in Scotland.
The Pope was greeted by enthusiastic crowds, particularly at tonight's Mass in Glasgow, where babies were passed to him to be blessed as he arrived in the Popemobile.
In his address at the Mass he made a reference to the size of the turnout, saying: "It is with some emotion that I address you, not far from the spot where my beloved predecessor Pope John Paul II celebrated Mass nearly 30 years ago with you and was welcomed by the largest crowd ever gathered in Scottish history."
An estimated 250,000 were present in 1982 compared with around 65,000 tonight, but church leaders in Scotland declared themselves delighted with the reception the Pope received.
After he was officially welcomed by the Queen at the Palace of Holyroodhouse in Edinburgh the Pope spoke of the UK's important place in history.
He said: "Your forefathers' respect for truth and justice, for mercy and charity, come to you from a faith that remains a mighty force for good in your kingdom, to the great benefit of Christians and non-Christians alike."
He cited anti-slave campaigners William Wilberforce and David Livingstone, and women such as Florence Nightingale, as examples of that force for good.
And he praised Britain's fight against Hitler's "atheist extremism", saying that "Britain and her leaders stood against a Nazi tyranny that wished to eradicate God from society and denied our common humanity to many, especially the Jews, who were thought unfit to live".
The Pope, who was forced to join the Hitler Youth as a 14-year-old schoolboy, said the UK remained "a key figure politically and economically on the international stage".
"Your Government and people are the shapers of ideas that still have an impact far beyond the British Isles. This places upon them a particular duty to act wisely for the common good."
And, referring to the future, he delivered an apparent warning about the risks to the nation's traditional values.
He said: "Today, the United Kingdom strives to be a modern and multicultural society.
"In this challenging enterprise, may it always maintain its respect for those traditional values and cultural expressions that more aggressive forms of secularism no longer value or even tolerate."
The Glasgow crowd had been warmed up by Britain's Got Talent star Susan Boyle who got a huge cheer when she took to the stage.
Wearing a long black coat and heels, Boyle, 49, sang the tune that catapulted her to fame, I Dreamed A Dream from the hit musical Les Miserables.
Pilgrims waved flags in the air as she sang.
The leader of Scotland's Catholics Cardinal Keith O'Brien expressed delight with the turnout in Edinburgh.
He told reporters: "Along Princes Street I really felt so proud.
"You could look to one side and see the backcloth of the castle and the ramparts and so on, and on the other side a sea of faces welcoming Pope Benedict XVI to our country.
"The Pope is a wonderful, warm, friendly character, radiating a certain calm and a certain peace from him, and the respect which was being shown him, and just the love that was radiating to him from the people who were lining along Princes Street.
"I think that he's aware of all that has been done to make him so welcome from everybody in our country, from the First Minister in the Scottish Government down to the smallest school child."
Speaking on a visit to Brussels, Prime Minister David Cameron said: "I would like to offer Pope Benedict a very warm welcome to Britain for this incredibly important and historic visit.
"It is the first ever official papal visit to our shores. It is a great honour for our country.
"This will be a very special four days, not just for our six million Catholics, but for many people of faith right across Britain, and millions more watching around the world.
"It is a great opportunity to celebrate the enormous contribution that all faith communities make to our society."
Lothian and Borders Police estimated that a total of 125,000 people had lined the streets for the procession along Princes Street.
But not everyone was welcoming.
Around 20 protesters gathered at the designated demonstration, their complaints ranging from abusive priests to the Pope's stance on contraception and homosexuality.
Among the dissenting voices was the Reverend Ian Paisley, now Lord Bannside, who mounted a similar protest in Liverpool in 1982 for the visit of Pope John Paul II.
Dr Paisley criticised the fact that the visit was not discussed in the House of Commons, adding that the "whole thing is nonsense".
Terry Sanderson, president of the National Secular Society, criticised the Pope's comments on secularism, saying: "British people have embraced a secular identity of their own free will, perhaps as a reaction to the ultra-conservatism of this recent papacy and the extremism that has been manifested by some forms of Islam.
"The secular identity of the British people is not something to criticise, but to celebrate."