0112 GMT September 24, 2018
The Washington Post gave an account of meetings Attorney General Jeff Sessions held with the Russian ambassador to the US, Sergey Kislyak.
Sessions has previously denied discussing the election campaign, BBC reported.
US authorities are investigating possible collusion between Russia and the Trump team.
The intelligence services believe Russia meddled in the vote to help Trump win. Russia denies this, and Trump says there was no collusion.
The Post's report quoted current and former US officials who cited intelligence intercepts of Kislyak's version of the encounter to his superiors.
One of those quoted said Kislyak spoke to Sessions about key campaign issues, including Trump's positions on policies significant to Russia.
During his confirmation hearing earlier this year, Sessions said he had no contact with Russians during the election campaign. When it later emerged he had, he said the campaign was not discussed at the meetings.
An official confirmed to Reuters the detail of the intercepts, but there has been no independent corroboration.
The officials spoken to by the Post said that Kislyak could have exaggerated the account, and cited a Justice Department spokesperson who repeated that Sessions did not discuss interference in the election.
But the Post's story was the focus of one of many tweets the US president fired off on Saturday morning.
"A new INTELLIGENCE LEAK from the Amazon Washington Post, this time against A.G. Jeff Sessions. These illegal leaks, like Comey's, must stop!" Trump said.
The Washington Post is owned by Amazon, whose founder Jeff Bezos has been an occasional sparring partner for Trump. "Comey" refers to James Comey, the former FBI boss Trump fired.
Earlier this week, Trump told the New York Times he regretted hiring Sessions because he had stepped away from overseeing an inquiry into alleged Russian meddling in the US election.
Sessions recused himself in March amid pressure over his meetings with Kislyak. He says he plans to continue in his role as attorney general.
Several other regular targets for Trump featured in his series of tweets.
He accused the "failing" New York Times of foiling an attempt to assassinate the leader of the Islamic State group, Abu Bakr al-Baghdadi.
It is not clear what Trump was referring to, but on Saturday a US general complained on Fox News that a "good lead" on Baghdadi was leaked to a national newspaper in 2015.
A New York Times report at the time revealed that valuable information had been extracted from a raid, but the paper stressed on Saturday that no-one had taken issue with their reporting until now.
Trump also said he had "complete power" to pardon, amid reports he was considering presidential pardons for family members, aides and even himself in response to the Russian investigation.
And he again urged Republicans to "step up to the plate" and repeal and replace President Obama's healthcare reforms, a key campaign pledge of his that has collapsed in Congress.