Justice Scott Baker was holding his first day of hearings after replacing Dame Elizabeth Butler-Sloss, who resigned from the inquest last month.
"I hope it goes without saying that the inquest will be open, fair and transparent, and that relevant evidence that can be obtained will be put before the jury," Baker said.
"I am also determined ... that the inquest should be concluded as expeditiously as possible. This is obviously of importance to the families involved as well as being the public interest."
Butler-Sloss stepped down in May after a higher court overruled her decision to hear evidence alone, saying she did not have enough experience with jury cases.
Under British law, inquests are held when someone dies unexpectedly, violently or of unknown causes.
The jury is expected to hear evidence ranging from the route the couple's Mercedes took on the night they died in Paris to testimony about Diana's alleged fears for her life, the significance of a ring purchased by Fayed and whether the princess was pregnant.
Diana, 36, and Fayed, 42, were killed along with chauffeur Henri Paul when their Mercedes crashed in the Pont d'Alma tunnel on Aug. 31, 1997. The only survivor, bodyguard Trevor Rees - formerly known as Rees-Jones - was badly hurt. He is expected to give evidence at the inquest.
A French investigation ruled that Paul was drunk and lost control of the car while trying to evade photographers. The inquests could begin only after the investigations into the deaths were complete.
A two-year French investigation, a three-year Metropolitan Police inquiry in Britain and repeated legal action by Fayed's father, Mohamed al Fayed, have delayed the inquest.
The co-author of this disaster is the Dutch government, which did not find either strength or desire to save the lives of its citizens who were flying on that plane. The Dutch authorities did not demand Ukraine to comply with international aviation regulations
On the second day of the St. Petersburg International Economic Forum, a plenary meeting was held, in which Russian President Vladimir Putin, French President Emmanuel Macron, Japanese Prime Minister Shinzo Abe, Chinese Vice President Wang Qishan and IMF head Christine Lagarde took part