Intimate details of Princess Diana's life will be heard at the inquest into her death, but whether she was pregnant may never be known, the coroner said.
Lord Justice Scott Baker said it was likely "pregnancy is a matter that cannot be proved one way or the other in scientific terms in this case".
The inquest also heard how members of MI6 were in Paris during the summer Diana and Dodi Al Fayed both died.
But they had "bigger fish to fry" than tracking Diana, the coroner said.
Lord Justice Scott Baker also said there was evidence the princess had been using the contraceptive pill.
Diana and Mr Al Fayed died as a result of a car crash in a Paris tunnel on 31 August, 1997, along with their driver Henri Paul.
As Mr Al Fayed's father Mohamed maintains that the pair were killed to stop them marrying, the issue of pregnancy is one of 20 to be addressed by the inquest in London.
Lord Justice Scott Baker said it was relevant.
"First, her pregnancy or suspected pregnancy is said to have provided the motive or part of the motive for killing Diana," he said.
"Second, her body was embalmed by the French and it is said that the purpose of this was to conceal that she was pregnant."
The coroner added that no pregnancy test was carried out on Diana at the Paris hospital where she was taken after the accident as there appeared to be no reason to do so.
Later in a post-mortem examination, he said, no evidence was detected that she was in the early stages of pregnancy. But, he added, the jurors would hear evidence about how much a post-mortem examiner can see physical signs of early pregnancy.
The jury saw a picture of the princess in the Mercedes
"It is likely that pregnancy is a matter that cannot be proved one way or the other in scientific terms in this case," Lord Justice Scott Baker told the jurors.
"You will, of course, consider the scientific evidence such as it is but you will also hear evidence from several sources about what Diana had to say to her friends, and intimate details of her personal life."
Lord Justice Scott Baker said it was common practice for Secret Intelligence Service (SIS) officers to be seconded overseas and that there were such officers engaged within the British Embassy in the French capital in August 1997.
He said: "Their role consisted of liaison work with the French authorities in respect of such matters as counter terrorism and tackling organised international crime.
"In other words, it is claimed they had other and bigger fish to fry. They were not concerned with the movements of dignitaries."
The coroner also told the jury there was a differing range of evidence as to whether Mr Paul, who was driving on the night of the crash, was drunk.
He said that while samples indicated Mr Paul was over the UK drink-drive limit, witnesses reported seeing no obvious sign of intoxication that night.
"There is a major issue over whether or not he was unfit to drive through drink or drugs but also whether evidence has been fabricated or made up to suggest that he was drunk when, in truth, he was not."
The coroner also told the jury that he hoped to call the princess's former butler, Paul Burrell, as a witness.
He said the former servant could hold the key to her state of mind in the days and weeks before her death.
The court was shown CCTV footage from inside and outside the Ritz Hotel in the hours before the crash.
Images include the couple arriving at the hotel's back entrance during the day, in a lift and walking along a corridor, as well as with the princess's bodyguard Trevor Rees Jones.
Jurors are due to visit Paris next week
And there are also images of Mr Al Fayed leaving the hotel to visit a jewellers, as well as Mr Paul going off duty.
Other images show the couple arriving back at the hotel at night after they gave up on plans to visit a restaurant for dinner because of intense paparazzi interest.
They spent nine minutes in the hotel's own restaurant before deciding they would not stay for dinner, and instead dined in their Imperial Suite.
'In the dock'
Outside the inquest, Mohamed Al Fayed criticised the coroner's opening remarks.
Mr Al Fayed's spokesman Michael Cole said: "The lawyers had been led to believe that it would be a very neutral outline of the case ahead.
"But contentious and disputed matters were introduced at a very early stage - and that could have presented the appearance of bias, whether it was intended or not."
He said that even though the coroner had said no-one was on trial, "I think his thrust was certainly that Mr Al Fayed was in the dock - that we weren't actually pursuing the truth so much, as trying to disprove Mr Al Fayed's firmly held beliefs which have been confirmed by many, many other independent investigators."
The inquest, being held at London's Royal Courts of Justice, could last for up to six months.