Trump was impeached in December over allegations that he improperly pressured Ukraine to announce an investigation into Burisma and its links to former board member Hunter Biden, the son of the president's election rival Joe Biden.
"The attacks were successful", Oren Falkowitz, a co-founder of Area 1 who previously served at the National Security Agency, told the Times.
Cybersecurity experts at California-based Area 1 Security released a report on January 13 that found Burisma Holdings, where the son of presidential front-runner Joe Biden sat on the board, was successfully penetrated in a wide-ranging phishing campaign that stole e-mail credentials of employees.
The alleged Russian hackers have repeatedly made headlines in Western media since 2016.
The hiring of Hunter Biden by the gas company has prompted criticism, including from defenders of Trump.
An anonymous whistleblower filed a complaint that Trump pressured Zelensky to investigate the Bidens, with the president vowing to withhold United States military aid to Ukraine until Kiev complied with his demand - a claim that had triggered the impeachment, with dozens of witnesses against the U.S. president.
It also resembles the tactics the Kremlin used to get emails from Hillary Clinton's campaign chairman and the Democratic National Committee in the 2016 election cycle. This is indeed exactly what Bob Mueller warned about in his testimony: "That the Russians would be at this again", Schiff said on MSNBC Monday night, referring to the special counsel who investigated Russia's attempts to interfere in the 2016 election and whether there was any coordination with the Trump campaign. Now, in a situation with echoes of the 2016 election, the New York Times reports that a security firm claims it has detected successful phishing attacks on Burisma by hackers connected to Russian Federation.
Burisma did not immediately respond to a request for comment.
Area 1 said it became aware of the Russian targeting of Burisma after its email security scanning product found suspicious evidence online, including "decoy domains" - websites created to imitate legitimate email services used by Burisma's subsidiaries.
Area 1 linked the hack - a "phishing" attack - to Russia's military intelligence unit known commonly as the GRU. Kvartal 95 was founded by Ukrainian President Volodymyr Zelenskiy and multiple employees of the station have since joined his administration.
President Trump is now due to stand trail in the Senate on two articles of impeachment - abuse of power and obstruction of Congress.
The phishing technique used is described as credential harvesting and involves stealing account information like usernames and passwords. Trump is seeking reelection and Biden is a potential opponent out of a dozen Democrats seeking their party's nomination.
Biden campaign spokesman Andrew Bates said the report "proves that both Donald Trump and Vladimir Putin understand the true stakes of this election".
"Donald Trump tried to coerce Ukraine into lying about Joe Biden and a major bipartisan, worldwide anti-corruption victory because he recognized that he can't beat the vice president", spokesman Andrew Bates said.
Neither Joe Biden or Hunter Biden were summoned to the US House to testify in Trump's impeachment.