Trump's public statement comes amid an impeachment inquiry in the Democratic-controlled US House of Representatives stemming from his efforts to push Ukraine's head of state to undertake a probe of the Bidens' business dealings in the Eastern European country, Efe news reported.
"China should start an investigation into the Bidens because what happened in China is just about as bad as what happened with Ukraine," Trump told reporters at the White House before flying to Florida for a campaign event.
Asked whether he had asked Chinese President Xi Jinping to assist with an investigation of the Biden family, Trump said he had not yet done so but that "it's certainly something we can start thinking about".
The Biden campaign on Thursday slammed Trump for calling on China and the Ukraine to investigate the candidate and his family.
"Now, with his administration in free-fall, Donald Trump is flailing and melting down on national television, desperately clutching for conspiracy theories that have been debunked and dismissed by independent, credible news organizations," Deputy Campaign Manager and Communications Director Kate Bedingfield said in a statement.
"It could not be more transparent: Donald Trump is terrified that Joe Biden will beat him like a drum" in the 2020 presidential election, she added.
Biden has said on multiple occasions that he had never had any discussions with his second son, Hunter Biden, about the latter's overseas business dealings, which have been the subject of numerous stories in the US media.
In an interview in July with the magazine The New Yorker, Hunter Biden defended himself from accusations that he had accepted a bribe two years ago from a Chinese magnate.
According to that magazine, during a dinner in May 2017 in Miami with Chinese businessman Ye Jianming, Hunter Biden offered to "use his contacts to help identify investment opportunities for Ye's company, CEFC China Energy, in liquefied-natural-gas projects in the United States."
The magazine said that at the time Biden was on the board of a non-profit that generates support for the United Nations' World Food Programme and that he had hoped that Ye would make a large aid donation
The story went on to say that after the dinner Ye sent Hunter a 2.8-carat diamond (estimated to be worth around $80,000) along with a card thanking him for the meeting.
Asked by The New Yorker if he thought the diamond was intended as a bribe, Biden said, "no."
"What would they be bribing me for? My dad wasn't in office."
Hunter told the magazine that he gave the diamond to his associates and does not know where it is now.
"I knew it wasn't a good idea to take it. I just felt like it was weird," he said.
After that dinner, Hunter began negotiating a deal for CEFC to invest $40 million in a liquefied-natural-gas project on Monkey Island, in the US state of Louisiana, according to The New Yorker, which noted that Ye was subsequently detained in February 2018 by Chinese authorities - reportedly as part of an anti-corruption investigation - and the deal with Hunter fell through.
Questions also have been raised in the media about Hunter Biden in regard to a large investment of Chinese capital in 2013 in a private-equity fund - BHR Partners - on whose board he sat. That investment came shortly after Hunter had visited the Asian country with his father, who was vice president at the time.
However, a spokesman for Hunter Biden said the former vice president's son did not acquire an equity interest in that fund until after his father had left office.
Last week, the speaker of the US House of Representatives, Democrat Nancy Pelosi, announced the start of an impeachment inquiry targeting Trump over alleged wrongdoing in a July 25 telephone conversation with Ukrainian President Volodymyr Zelensky.
That inquiry was launched after an anonymous whistleblower (reportedly an intelligence officer who was not a direct witness to the call) filed a complaint alleging that Trump had used the power of his office to solicit interference from a foreign country in the 2020 election.
In a rough transcript of the call that Trump released, the president urges Zelensky to look into former Vice President Biden's alleged interference in a probe of Hunter Biden's business dealings in Ukraine.
"There's a lot of talk about Biden's son, that Biden stopped the prosecution and a lot of people want to find out about that so whatever you can do with (US) Attorney General (William Barr) would be great," the transcript cites the president as saying.
Hunter began serving as a paid board member of Ukrainian natural gas company Burisma Holdings in 2014 while his father was Barack Obama's vice president.
"Biden went around bragging that he stopped the prosecution so if you can look into it ... It sounds horrible to me," Trump says on the transcript, although the boast in 2018 by the former VP concerned getting rid of a Ukrainian prosecutor viewed by many Western nations as soft on corruption.
Trump had temporarily frozen nearly $400 million in military aid to Ukraine just ahead of his call with Zelensky, prompting suspicion that the request to investigate the Bidens was linked to the release of the funds.
Trump vehemently denies that any quid pro quo was at work and says he withheld the aid over frustration with the amount of monetary assistance provided to Ukraine by other countries.
The aid was eventually released on September 11.
( With inputs from IANS )