In the letter, which was made public on Wednesday, Yanukovych urges the US leader to "take urgent and exhaustive measures to stop the war."
"I wrote to President Trump and told him the war needs to end," he told reporters in Moscow ahead of the letter's release.
The pro-Moscow president, who now lives in Russia, blames the conflict on "short-sighted and irresponsible actions by the Ukrainian and Western politicians."
"I request you take action in defence of... Human rights in Ukraine, restoration of democracy and rule of law," he wrote.
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Yanukovych was toppled by a pro-European uprising in February 2014 and fled the country with help from Moscow after parliament declared he had failed to fulfil his duties as president.
Protesters had begun gathering on Kiev's central square, known as Maidan, in November 2013 after Yanukovych rejected an association agreement with the European Union and opted to align himself more closely with Moscow.
In his letter to Trump, Yanukovych repeated his claims that "unidentified snipers" attacked both police and protesters.
"I have additional evidence and data that can help to identify the real masterminds of the mass killings on Maidan," he said.
After pro-European leaders took over in Ukraine, Russia annexed Crimea and a separatist conflict broke out in the mainly Russian-speaking east.
Yanukovych told Trump that officials from then-president Barack Obama's administration had "actively interfered in the situation, taking the side of the protesters."
Yanukovych said he now lives in the Rostov region of southern Russia, where he gave news conferences soon after leaving Ukraine. His Moscow press event took place under heavy security.
"I don't want to take revenge on anyone," Yanukovych said. "I dream of Ukraine being at peace and of normal life starting there.