Scientists say the Voyager 1 spacecraft is near the outer limit of the Solar System, 26 years after its US launch.
Voyager I is the most distant man-made object from Earth
The boundary is a region called "termination shock" where particles from the Sun begin to slow down and clash with atomic matter from deep space.
Nasa says Voyager 1 is about 13.5bn kilometres from Earth and will not reach another system for 40,000 years.
The spacecraft carries greetings in 55 languages and audiovisual materials
depicting life on Earth.
Beyond the ever-shifting termination shock boundary, lies a region called the heliopause, that marks the beginning of interstellar space.
Whether Voyager 1 has reached the first boundary or is still on approach remains unclear as, scientists provided evidence for both possibilities on Wednesday.
"This is very exciting: Voyager is beginning to explore the final frontier of our Solar System," said Edward Stone, a Voyager project scientist based at California Institute of Technology.
"It's a totally new region we've never been in before."
Voyager 1 was only meant to survive five years in space when it was launched in 1977 and yet since then it has been sending back a steady stream of data, including spectacular photographs of the Solar System.
Conflicting arguments about its progress appear in this week's Nature journal which admits in an editorial that no-one can yet be sure of the truth.
Louis Lanzerotti of Bell Laboratories and the New Jersey Institute of Technology said his team had found "compelling argument" that Voyager I was "in the vicinity of the termination shock" and had even passed briefly into the heliopause.
However, according to Frank McDonald of the University of Maryland, the probe was "not there yet".
"We say what we are seeing is exactly what we would expect to see as we approach the shock," he added.
What is certain is that the unmanned probe - which is being closely followed by Voyager II - is still functioning. It is currently 13.5 billion kilometres (8.4 billion miles) from the Sun, or 90 times the distance separating the Earth from the Sun.
"We do have enough electrical power; if nothing breaks on the spacecraft, we can continue till 2020," said Dr Stone.
If, as expected, Voyager I does cross the heliopause and passes into uncharted deep space, it may actually outlive its home planet.
The craft is carrying a time capsule in the form of a golden gramophone record, complete with stylus, which contains a recording of greetings from Earth in different languages as well as samples of music ranging from Mozart to singer Blind Willie Johnson.
Further observations from Voyager 1 should resolve the dispute, as well as provide information about a never-before-probed region of space.
Solar wind: Stream of charged particles blown off the Sun and travelling at supersonic speeds
Termination shock: Area where particles from the Sun begin to slow and clash with matter from deep space
Heliosheath: A vast, turbulent expanse where the solar wind piles up as it presses outward against interstellar matter
Heliopause: The boundary between the solar wind and the interstellar wind, where the pressure of both are in balance
Bow shock: The shock wave caused by the edge our Solar System travelling through deep space