The performance artist is spending 512 hours interacting with the public at the show, held in three completely empty rooms.
Phones, cameras and even watches are banned, as Abramovic takes people by the hand and encourages them to spend time focusing on the bare white walls.
"Take in the silence," she whispered to one. "Just be present."
After half-an-hour, the gallery was filled with human statues, manoeuvred into position by the Belgrade-born artist and her team of six "guards", all clad in black.
Participants closed their eyes and rocked on their heels, some assumed meditative positions, while others followed Abramovic around, hoping for a personal interaction.
"I really wanted to connect with her, so I said a little prayer," said Sophie, a student sculptor from London.
"Connecting with her presence was really special. She said, 'stay here as long as you like, take deep breaths, be present'.
"It was perfect, really."
Entry to the exhibition, which lasts for 10 weeks, is free but only 160 people can be admitted at a time. Each can stay as long as they wish, with the gallery imposing a "one in - one out" policy.
Abramovic herself opened the gallery doors at 10:00 BST - as she will every day - by which point there were already hundreds of acolytes and art lovers queuing in Kensington Gardens.
Geraldine, an art professor from Kensington, had arrived at 06:30 BST to be amongst the first to see the performance.
"It was like being at a very beautiful party where nobody talks," she told the BBC. "It may push me into doing some meditation, which is probably very good for me, so it changed my life in a very positive way."
"Just to sit and get lost in one's thoughts, I think it's very relaxing," said Andrew, a psychiatrist visiting the UK from San Francisco.
"And certainly some people were crying, too, so perhaps it brings up some thoughts that one pushes down from normal life."
The show is titled 512 Hours, after the amount of time Abramovic will spend in the gallery.
It is her first performance work since The Artist is Present, at the Museum of Modern Art in New York, where she sat motionless, six days a week, looking directly at whoever sat down in a chair placed opposite her.
Both shows lack the startling drama of her earlier performances, including one in which she systematically stabbed her hand with knives.
In another, she whipped herself, before cutting a five-point star in her stomach with a razor blade and lying on a cross made of ice.
Once, she nearly died after lying in the middle of a burning cross made of petrol-soaked sawdust. On another occasion, she allowed an audience member to hold a loaded gun to her head.
Nonetheless, she told the BBC her latest show "really frightens me".
"I worry about the British public," she said, adding that the public's cynicism might get in the way of creating "a pure emotional connection".
"My only chance with the British public is to be vulnerable," she told Radio 4's Front Row. "The audience is someone who completes the work."
Ahead of the show, the 67-year-old was accused of failing to acknowledge other artists who engage in the "art of nothing".
Two weeks ago, a  group of US art historians curators wrote to the Serpentine, asking it to recognise the influence of Mary Ellen Carroll. a conceptual artist who has been working on a project called "Nothing" since 2006, when she went to Argentina with only her passport.
But Abramovic dismissed the accusations, telling the BBC: "There is nothing on the walls of the gallery, no work. But I am working eight hours a day with the energy of the public."
During the first hour of the first day of her performance, Abramovic seemed to be playing a giant game of cosmic yogic chess, with the public as her pieces, positioned carefully throughout the gallery.
There was something eerie about entering a room full of bodies frozen in space but, once guided into position, most of the visitors reported feeling an overwhelming sense of wellbeing.
"I started seeing the sky - the clouds in the sky - in the white of the wall," said Chester, a TV producer who had skipped work to attend the opening.
"It was a religious experience. I think you'd have to sum it up as that."
Abramovic says the performance will evolve over the course of its 10-week run.
"Maybe it's complete silence, maybe we all scream together, maybe we all lie on the floor.
"Everything is there, in possibility. We need the public, we need me, and we need chemistry."
512 Hours runs at the Serpentine Gallery in London until 25 August.
Audience members were moved to tears at the opening of Marina Abramovic's new show at London's Serpentine Gallery.