WASHINGTON – Senate Judiciary Committee Chairman Lindsey Graham sent a letter to Secretary of State Mike Pompeo on Thursday requesting documents related to former Vice President Joe Biden and his communications with Ukrainian officials, a step seen as a GOP effort to counter the House impeachment investigation of President Donald Trump.

The inquiry by Mr. Graham, R-S.C., is focused on any calls Mr. Biden may have had with Petro Poroshenko, then the Ukrainian president, regarding the firing of the country’s top prosecutor, as well as any that referenced an investigation of Burisma, the Ukrainian natural-gas company that employed Mr. Biden’s son Hunter Biden.

Mr. Graham’s document request suggests he is seeking to legitimize Mr. Trump’s accusations that Mr. Biden, then vice president, put pressure on Ukraine to fire its lead prosecutor to protect his son, a claim without evidence that has been disputed by officials familiar with the investigation.

BREAKING: @LindseyGrahamSC demands from @StateDept the transcripts of the calls between fmr VP @JoeBiden and the fmr Ukrainian President. || #Burisma #HunterBiden

More: https://t.co/cWChhALGS6 pic.twitter.com/uNtv3yAsJA

— Sara A. Carter (@SaraCarterDC) November 21, 2019

Mr. Graham, one of Mr. Trump’s fiercest defenders on Capitol Hill, told The Washington Post in late October that he was under intense pressure to launch an investigation into Mr. Biden by Mr. Trump and his allies.

But he said he would not “turn the Senate into a circus” and would instead focus his committee’s work on the investigation into the Justice Department’s launch of the Russia investigation.

Taylor Reidy, a spokeswoman for Mr. Graham, said the senator is now seeking the documents because “Adam Schiff and the House Intel Committee have made it clear they will not look into the issues about Hunter Biden and Burisma.” Rep. Schiff, D-Calif., is chairman of the House Intelligence Committee.

Did the whistleblower help arrange phone call between former VP Biden and the former President of Ukraine (Poroshenko) complaining about prosecutors behavior toward Burisma, the Ukrainian gas company where Hunter Biden was a member of the board?

— Lindsey Graham (@LindseyGrahamSC) November 13, 2019

“Graham is requesting documents which could shed additional light on that issue and hopes they will be able to answer some of the outstanding questions,” she said.

In Mr. Graham’s letter to Mr. Pompeo – seemingly timed to coincide with the conclusion of the public impeachment-inquiry hearings in the House – he asks for communications between Joe Biden and Mr. Poroshenko as well as any between Devon Archer, a business partner of Hunter Biden’s, and then-Secretary of State John Kerry on March 2, 2016, based on reporting that the two were scheduled to meet that day.

A former Kerry aide, who requested anonymity to speak about a private meeting, said that the meeting was “100 percent unrelated to Burisma” and included “no mention of business.” The aide characterized the meeting as a “courtesy hello to a 2004 alumni” of Kerry’s presidential campaign and said their exchange lasted no more than five minutes.

Mr. Graham does not provide a deadline for the State Department to produce these documents.

The unsubstantiated allegation that Joe Biden acted nefariously in pushing for the removal of Ukraine’s prosecutor is at the center of the impeachment inquiry into Mr. Trump. Mr. Trump asked Ukrainian President Voldodmyr Zelenskiy in a July 25 phone call to look into the Bidens – an attempt, Democrats charge, to use his power to strong-arm a foreign leader into investigating a potential political opponent.

When Mr. Biden pressured Ukraine to fire its prosecutor by threatening to withhold $1 billion in U.S. loan guarantees, he was leading a charge supported by the Obama administration, many Western leaders and several Republican senators.

Throughout the House hearings, Republicans have sought to shift the narrative to focus on the Bidens. They asked for Hunter Biden to testify, a request the Democrats rejected as irrelevant to the question of whether Mr. Trump abused his power.

Kurt Volker, a former envoy to Ukraine who Republicans asked to testify publicly, said during his hearing Tuesday that “allegations against Vice President Biden are self-serving and not credible.”