Tatyana Anodina, the head of the inter-state air committee, which investigates crashes in Russia, said: "It has been established that in the cockpit there were individuals who were not members of the crew.
"The voice of one of them has been identified exactly, the voice of the other, or the others, will require additional information from the Polish side."
She said the issue required further examination and she declined to draw any conclusions.
Speaking after weeks of analysis of the aircraft's "black boxes" - voice and data recorders - by international specialists, Anodina did not comment on the identities of the individuals in the cockpit.
The Polish news agency PAP, quoting a source close to the investigation, said one of the voices was Andrzej Blasik, the commander-in-chief of the Polish air force.
All 96 people on board, including Kaczynski, his wife and scores of senior Polish officials were killed in the crash in heavy fog outside the western Russian city of Smolensk.
There had been media speculation that a high-ranking member of the Polish delegation could have ordered the pilots to land, although until now this had so far been dismissed by investigators on both sides.
Russian and Polish investigators are continuing to investigate the cause of the crash.
Edmund Klich, the Polish representative to the investigation committee, said the individuals had been in the cockpit 16 to 20 minutes before the crash.
"I do not think this had a decisive effect on the causes of this event. But this is my personal opinion and only after a full investigation of all the circumstances will this be clear," he said.