He said in an earlier tribute, "My thoughts are with the royal family, those she loved and all those who loved her. She leaves an incomparable legacy and will be profoundly missed."
Craig looked back on filming a skit for the Olympic Games opening ceremony in London in 2012. It saw the actor, 54, who has played 007 in five consecutive films, drop in at Buckingham Palace to meet with the Queen.
Sitting at her writing desk, the Queen then turned and greeted him: "Good evening, Mr Bond."
Along with some of her pet corgis, the pair then walked to a helicopter and set off for the Olympic Stadium, as a stunt double of the monarch parachuted into the arena.
Moments later, the Queen herself, dressed to match the stunt double, entered the stadium amid deafening applause.
Prior to her death on September 8, Craig told The Late Show with Stephen Colbert what she was really like behind closed doors.
"Very funny. Very funny. [She] wants to crack a joke, and [she] cracked a joke about me," he recalled.
"We were having our photographs taken and she just went, 'Oh no, he's the one that doesn't smile. Fair enough!'"
Speaking about their Olympic Games skit, he said it was originally supposed to be serious.
"She was fun, incredibly game. We had a short space of time and I was a bit grumpy as it was my day off and suddenly I am at the Palace with the Queen at her private chamber," he said.
"And she improvises a little bit. She was supposed to be sitting at the desk and she asked if she could write, so she pretended to write."
