In a message to mark today's 25th anniversary of the worst terrorist atrocity over British soil, the Prime Minister also described his "unconditional" admiration for the families and friends of those killed. "For the fortitude and resilience you have shown. For your determination never to give up. You have shown that terrorist acts cannot crush the human spirit," he said.
"That is why terrorism will never prevail."
His words will be read out at a memorial service in Arlington National Cemetery near Washington DC, one of a number of events being held on both sides of the Atlantic, including in Lockerbie, Westminster Abbey and at Syracuse University in upstate New York, which lost 35 students in the bombing.
A total of 270 people died when Pan Am Flight 103 exploded over Lockerbie on December 21, 1988.
First Minister Alex Salmond is due to attend a wreath-laying ceremony and memorial service at Dryfesdale cemetery in Lockerbie, alongside Lord Wallace, the Advocate General for Scotland.
Last night, he said the atrocity was a memory that remained "sharp for anyone who was living in Scotland at the time".
He added: "On this 25 year anniversary, and as the country prepares once more to relive the harrowing events of that terrible night, it is important we remember that the pain and suffering of the families and friends of those who died has endured since that winter night in 1988."
The Moderator of the General Assembly of the Church of Scotland, the Rt Rev Lorna Hood, who will take part in the Westminster Abbey service, said she vividly recalled the days after the bombing. "I remember so clearly the devastation of the town and the grief and sorrow of relatives who journeyed across the Atlantic to see the spot where their loved ones died," she said.
"For weeks after, rescue workers, police, members of the forces and civilians worked tirelessly to recover as much evidence as possible from the wreckage and to this day live with difficult memories of that time."
She added she knew for many there were still unanswered questions about the atrocity, but the anniversary was a "time to remember the 270 innocent lives cut short and the families here in Scotland and the USA living with that loss".
"It is also a time for us to pray for a world where we can live together in peace, travelling to different parts of our world in confidence and safety, appreciating our differences, but rejoicing in all that unites as human beings," she said.
That sentiment was echoed by Scotland Office Minister David Mundell, who will read out the Prime Minister's message at the service in Arlington. In the cemetery stands a cairn of red sandstone, one brick for every life lost in the atrocity.
The blocks came from Corsehill Quarry in Annan, Dumfriesshire.
Mr Mundell said: "Much of the focus has been on the perpetrators, however it is especially important to think of those who lost their lives or were caught up in the events and had their lives shaped by that fateful night."
In Arlington and Lockerbie wreaths will be laid by the Lord Advocate Frank Mulholland and the Solicitor General Lesley Thomson. They will bear the message, repeated in Gaelic: "Always remembered, Never forgotten, Forever in our hearts".
Labour leader Ed Miliband described the bombing as a horrific act carried out as many of those killed were on their way to meet loved ones. Many of the victims were travelling to visit family and friends for Christmas.
"Our thoughts are with all of those who died and with the people who lost loved ones 25 years ago - many of whom campaigned passionately for justice for the victims."
Deputy Prime Minister and Liberal Democrat leader Nick Clegg said: "On this anniversary, we stand with these brave individuals and families to remember those who died. And we dedicate ourselves to learn from their example: committing always to meet the worst of human nature with the very best of human nature."
In 2001, Abdelbaset al Megrahi became the only person convicted of the Lockerbie bombing. He was given a life sentence that year, but diagnosed with incurable prostate cancer in 2008 and eventually told he had just three months to live.
This prognosis led to a highly controversial decision by Scottish ministers to free him under compassionate release rules.
This sparked a high-profile row between politicians on both sides of the Atlantic. Megrahi died in Tripoli in May last year.
His release, as well as his conviction, proved to be controversial.
A number of the British relatives of those killed believe he was innocent and are considering another appeal against the conviction when they meet with lawyers in the new year.