Senator Lindsey Graham has said Department of Justice officials have created a “process” enabling Rudy Giuliani to provide them with “information from Ukraine”, for further investigation.

Graham, a top ally of Donald Trump who was part of the successful vote to acquit him in his impeachment trial last week, cautioned that this information from the president’s personal lawyer “could be Russian propaganda”.

“The Department of Justice is receiving information coming out of the Ukraine from Rudy,” Graham said, explaining that the US attorney general, William Barr, “told me that they’ve created a process that Rudy could give information and they would see if it’s verified”.

Giuliani was deeply implicated in Trump’s efforts to get Ukrainian officials to help his 2020 re-election bid – the matter at the heart of the impeachment trial. Trump was impeached in the Democratic-led House after withholding military assistance, as well as a White House meeting, while calling for Ukraine announcing investigations into potential 2020 rival Joe Biden and his son Hunter.

Trump also wanted Ukraine to announce an investigation into the conspiracy theory that Ukrainian actors, not Russians, meddled in the 2016 election.

Almost immediately after Trump was acquitted by the Republican-led Senate last week, Republicans returned to investigating the unsubstantiated corruption allegations against the Bidens. There is no evidence of wrongdoing.

“Rudy Giuliani is a well-known man. He’s a crime fighter. He’s loyal to the president,” Graham also said. “He’s a good lawyer. But what I’m trying to say – to the president and anybody else – that the Russians are still up to it.”

In Graham’s interview on CBS’s Face the Nation, he revealed that his conversation with Barr took place earlier on Sunday morning. He also spoke with the Senate intelligence committee chair, Richard Burr. Both “told me: ‘Take very cautiously anything coming out of the Ukraine against anybody.’

“After talking to the attorney general and the intelligence chairman that any documents coming out of the Ukraine against any American, Republican or Democrat, need to be looked at by the intelligence services, who has expertise I don’t, because Russia is playing us all like a fiddle.”

Graham said “no” when asked if the justice department had been ordered to investigate the Bidens.

Graham also said the possibility of conflicts of interest involving the Bidens should be examined, but once again emphasized caution, saying: “When it comes to documents coming out of the Ukraine, to Republicans and Democrats, be very cautious turning … anything over you got over to the intel community.

“I’m telling Rudy, you think you got the goods? Don’t give it to me, because what do we know? We know that the Russian disinformation campaign was used against President Trump,” Graham also said. “They hacked into the DNC system. Not the Ukrainians, and they’re on the ground all over the world trying to affect democracy all over the world.”

“Who’s paying Rudy Giuliani?” host Margaret Brennan asked.

“ I don’t know,” Graham said. “Here’s my message to Rudy: if you’ve got something coming from the Ukraine, turn it over to the intelligence people, the Department of Justice, to any Democrat.”

Giuliani did not immediately respond to a request for comment. On Twitter this morning, Giuliani alluded to “two smoking gun documents” in a post urging people to subscribe to his podcast.