Seif al-Islam Gaddafi was caught yesterday in southern Libya after months on the run and his arrest sparked a wave of celebrations across the country.
Prosecutors from the International Criminal Court (ICC) are preparing to travel to Libya to negotiate with the new government about how the 39-year-old will be put on trial.
There are fears he could suffer the same fate as his father but Mr Burt said the British Government, while offering support, should not interfere in the process.
He told Dermot Murnaghan on Sky News: "We have got confidence in both the ICC and what we have heard from the Libyan authorities that between them they will be able to work out where a trial will be held and then it will be held under international standards and conditions.
"It's very important that Seif al-Islam does have a fair trial, that he answers the charges that have been levelled against him by the Libyan people and we will support that process.
"I think the new Libyan government does understand what is at stake here. They want to show that their government is different from the regime and this trial, this opportunity to demonstrate that, is very important for them.
"I honestly think at this stage that it is much too early and rather presumptuous for all of us to be telling them what to do. Safeguards are important but people are already on their way to work those out with the Libyan authorities.
"I think at this stage we should allow them to get on and do their job between them and work out where the best place for a trial would be with international conditions and plainly international observance and monitoring."
Mr Burt said the Government had also sought reassurances from the Libyan authorities that Seif al-Islam would receive a fair trial.
He added: "I think there is an issue of sovereignty involved. I think there is an issue of pride of what has been achieved in the revolution in Libya.
"These are people who understand what is at stake and are going to work with the International Criminal Court and we will provide all assistance to both to find the best answer as to now what to do with the trial and the facing of justice of Seif al Islam."
Shadow chancellor Ed Balls said Labour had "nothing to fear" about what might come out if there was a trial about the party's links with the Gaddafi regime.
Speaking to Mr Murnaghan, the senior Labour MP said there "was no doubt"
Tony Blair, Gordon Brown and the Foreign Office's intelligence experts thought at the time that talks with the Libyan regime about disarmament were a "positive step forward".
He added: "They went in to it with open eyes and the possibility of progress. Now clearly, Colonel Gaddafi ended up breaking agreements, not
making progress, and I don't think a Labour government or any government should have anything to fear from open disclosure.
"I know at that time the motive was the right motive, could you see disarmament and progress on peace. That was the right thing to do then."
ICC prosecutor Luis Moreno Ocampo will travel to Tripoli in the next few days to discuss arrangements for the trial, including where it will be staged.
Earlier, Prime Minister David Cameron offered support to the court and the Libyan government to ensure Seif al-Islam faces justice for his role in the "barbaric" reign of terror.
Mr Cameron said: "The Libyan government's announcement of Seif al-Islam's arrest shows we are near the end of the final chapter of the Gaddafi regime.
"It is a great achievement for the Libyan people and must now become a victory for international justice too.
"He could have contributed to a more open and decent future for his country, but instead chose to lead a bloody and barbaric campaign against his own people. The fate of the Gaddafis should act as a warning
to brutal dictators everywhere.
"Britain will offer every assistance to the Libyan government and the International Criminal Court to bring him to face full accountability and justice for what he has done.
"The Libyan government has told us again today that he will receive a trial in line with international standards, and it is important that this happens."
Seif al-Islam was flown to the city of Zintan in northern Libya
and is said to have confirmed that he was feeling okay to international
reporters on the plane, saying that injuries on his right hand were caused by a Nato air strike a month ago.
Gaddafi's heir apparent was a key member of his father's inner circle and proved to be following in his footsteps. In February he told Libyans on state-run television that "rivers of blood" would flow with "thousands" of deaths if the uprising did not stop.
His PhD from the London School of Economics (LSE) was shrouded in
controversy, even prompting the British ambassador to the US to deny claims that he helped the dictator's son with his thesis.
At the time, the Foreign Office confirmed that Sir Nigel Sheinwald met Seif a--Islam during his time at the LSE but said he did not play any part in the writing of his thesis.
In 2009, Seif al-Islam reportedly attended a shooting party at Lord Rothschild's Waddesdon Manor in Buckinghamshire, which was also attended by Lord Mandelson when he was Business Secretary.
Lord Mandelson and Seif al-Islam reportedly met at Lord Rothschild's villa in Corfu, days before the announcement that Lockerbie
bomber Abdelbaset Ali Mohmed al-Megrahi was to be freed on compassionate grounds.
Seif al-Islam later accompanied the dying terrorist back to Libya.
In London he apparently enjoyed a playboy lifestyle.
Two years ago he moved into a multimillion-pound house in Hampstead and threw a lavish party in Montenegro for his 37th birthday, to which Lord Rothschild and his business associate, Russian oligarch Oleg Deripaska, were reportedly invited.
PA
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