The lander, named Philae, was released from its mothership Rosetta on Wednesday (local time) as it orbited comet 67P/Churyumov-Gerasimenko, in the climax of a 10-year mission for the ESA.
But harpoons to anchor it to the surface failed to deploy and it bounced twice before floating to rest two hours later. The ESA needs to analyse data beamed half a billion kilometres (300 million miles) back to Earth to pinpoint its location.
"Where we are is not entirely where we wanted to be," lead lander scientist Jean-Pierre Biebring told a news conference.
The ESA has published pictures of the comet and images of the 100-kg (220-pound) lander - virtually weightless on the comet's rocky surface - and said it was operating normally.
"Do not put the emphasis on the failures of the system, it is gorgeous where we are now," Biebring said.
In the shadows, Philae's solar panels, which were meant to power the probe when its batteries run out on Friday, get only an hour and a-half of sunlight a day, instead of the expected six to seven hours.
The probe could try to use its landing gear to hop out of the shadows but ESA will need to know more exactly where it is before attempting the risky manoeuvre, scientists at the ESA's space operations centre in Darmstadt, Germany, said.
The lander also appears to have only two of its three feet on the ground, raising questions about whether it can drill without tipping over or pushing itself off into space.
Scientists hope that samples drilled from the comet by Philae will unlock details about how the planets - and possibly even life - evolved. The rock and ice that make up comets preserve ancient organic molecules like a time capsule.
Comets date back to the formation of the solar system some 4.6 billion years ago. Scientists suspect comets delivered water to Earth when they collided with the planet aeons ago.
The ESA said even without the drill, the Rosetta mission - which costs about 1.4 billion euros ($1.7 billion) - was relaying groundbreaking data and images.
