"It is just a fact that the Republican nominee for President was encouraging Russia to hack his opponent because he believed it would help his campaign," Xinhua news agency quoted White House spokesman Josh Earnest as saying during the daily briefing.
The remarks came one day after Earnest suggested on Wednesday's briefing that Trump was aware before Election Day that Russia was involved and "their involvement was having a negative impact on his opponent's campaign".
Senior Trump adviser Kellyanne Conway on Thursday took a shot at Earnest, calling his remarks on Wednesday "incredibly irresponsible".
"He essentially stated that the President-elect had knowledge of this (hacking), maybe even fanned the flames," said Conway in an interview with Fox News. "It's incredibly irresponsible and I wonder if his boss, President Obama agrees."
During his campaign, Trump at one of his news conferences in July did encourage the Russians to hack his rival Democrat Hillary Clinton's e-mail system and reveal the contents.
"I will tell you this, Russia: if you're listening, I hope you're able to find the 30,000 e-mails that are missing," said Trump, referring to half of the e-mails deleted from Clinton's private e-mail server because they were claimed by Clinton as containing private information.
The Trump team later characterised that remark as a joke.