It's unknown whether Putin responded to the letter, but Berezovsky did not return.
Putin has been told of Berezovsky's death, Peskov told Russian state television.
A declining fortune
Berezovsky was found Saturday afternoon by his bodyguard at his home in the affluent community of Ascot, Berkshire, west of London, said an official at Bell Pottinger, a public relations firm that represented Berezovsky.
The bodyguard told police he forced open a bathroom door that had been locked from the inside and found Berezovsky's body on the floor.
Berezovsky made headlines last year after losing what has been called one of the most expensive private lawsuits in history against a former friend and ally, Russian magnate Roman Abramovich.
Berezovsky sued Abramovich, owner of the Chelsea Football Club, for $5.1 billion, alleging that he was forced to sell his stake in the Russian oil company Sibneft for a fraction of its true value.
The judge called Berezovsky's testimony unreliable and, at points, dishonest.
The case raised a public curtain on the world of Russia's oligarchs.
Berezovsky's fortune has reportedly been on the decline in recent years, and it took a huge hit after he lost the case against Abramovich.
Analysts put the price tag for legal fees alone at more than $250 million spent between the two figures.
In recent weeks, reports emerged that Berezovsky was trying to sell pieces of his estate, including an Andy Warhol painting, "Red Lenin," to pay debts.
Damian Kudriavtsev, a friend of Berezovsky, said Sunday that his friend was unhappy and was in financial trouble, but wouldn't have harmed himself.
Berezovsky, he said, had always hoped to return to Russia someday.