"We treat any information on this case very seriously and we will also do so with these letters," said detective Peter Vacok, who is investigating the case which has rocked Slovak politics.
The letters, sent to Mr Vacok and some independent dailies, alleged that the state intelligence agency, the Slovak Information Service (SIS), had been involved in the kidnapping of Michal Kovac junior near Bratislava on 31August.
There was no confirmation whether the letters, written by an unnamed person, were genuine or a hoax.
But Mr Vacok said: "It would be natural that a person, afraid for his life would try to announce some important facts through the media."
Kovac junior was dumped in Austria and he is now out on bail waiting for a Vienna court to decide whether he should be extradited to Germany, where he is wanted on suspicion of fraud.
The abduction took place amid a feud between the President and the Prime Minister, Vladimir Meciar.
It has provoked speculation of SIS involvement. The SIS is headed by Ivan Lexa, a close Meciar ally and enemy of the President. The government has denied any involvement in the case.
In one of the letters, published by the newspaper SME on Wednesday, the writer said he had been the member of an SIS group ordered to follow Kovac junior since 28 August, and to help in the kidnapping three days later.
At the moment of the crime their SIS cars had blocked the road to help another group abduct Kovac junior.
"I don't know who the members of that other group were, I don't know even if they were from the SIS," he said.