Trump's request for an investigation into the Bidens, directed to Ukrainian President Volodymyr Zelensky in a July 25 phone call, has resulted in an impeachment inquiry against the American leader launched by the House Democrats, reports Xinhua news agency.
In the Washington Post opinion piece published on Saturday, Biden said Trump seeking help from foreign countries in order to "extract political favours" was an "abuse of power," which he claimed "is the defining characteristic of the Trump presidency".
"President Trump is abusing the power of the presidency and is wholly unfit to be President," Biden wrote in a direct attack on his 2020 election rival.
"He is using the highest office in the land to advance his personal political interests instead of the national interest."
A whistleblower complaint filed in late August by an unidentified intelligence official alleged that Trump asked Zelensky during the call to probe Biden and his son Hunter, who once worked for Ukrainian gas company Burisma Holdings that was accused of corruption.
There has so far been no evidence of wrongdoing by the Bidens.
However, the former Vice President, during an event in January 2018 at the Council on Foreign Relations, bragged about how he in 2016 successfully persuaded the Ukrainian authorities to sack the country's then prosecutor general, Viktor Shokin, who was investigating Burisma Holdings at the time.
Trump claimed that his intent to scrutinize the Bidens was out of concerns over corruption, not politically motivated or aimed at sabotaging the former Vice President's presidential campaign.
"As President I have an obligation to end corruption, even if that means requesting the help of a foreign country or countries," Trump tweeted Friday.
"This has nothing to do with politics or a political campaign against the Bidens. This does have to do with their corruption."
Biden, for his part, vowed in a combative tone at the end of his article: "You won't destroy me, and you won't destroy my family. And come November 2020, I intend to beat you like a drum."
Meanwhile, House Democrats have extended their impeachment inquiry. On Friday, House Oversight and Reform Committee Chairman Elijah Cummings issued a subpoena to the White House seeking documents related to Trump's interactions with the Ukrainian leadership.
In a letter to Acting White House Chief of Staff Mick Mulvaney, Cummings, Intelligence Committee Chairman Adam Schiff and Foreign Affairs Committee Chairman Eliot Engel ordered that the documents should be produced by October 18.
The subpoena came after the three committees separately sent a letter earlier on Friday seeking documents from Vice President Mike Pence as part of their investigation.
( With inputs from IANS )