The incident was recorded and posted onto YouTube on Tuesday.
"When I have a hit on my life, are you going to take responsibility for that?" asks Canadian-Israeli activist David Sheen as he follows Gysi down the corridor housing the Left party's parliamentary offices on the video. "Are you going to take responsibility for the threats on my life?"
Gysi then locks himself into the bathroom, yelling "Out! Get out of here!", as Sheen continues to shout after him.
The confrontation stemmed from a talk that Sheen was supposed to give with American author Max Blumenthal, a sharp critic of the Israeli state's conduct in the ongoing Israel-Palestine conflict, at Berlin's Volksbühne on the anniversary of Kristallnacht, November 9.
Gysi had also sought to prevent the pair from speaking to MPs in the Linke conference room at the parliament.
Upon the urgings of Green party politician and head of the German-Israeli partliamentary friendship group Volker Beck, Left party representative Petra Pau and Reinhold Robbe, the president of the German-Israeli Society, the theatre cancelled the talk.
The three politicians expressed concern that a talk by the known Israel critics would create a forum for anti-Semitism.
"On November 9 ... a very one sided discussion of the conflict in the Middle East is being held by the Israel critics Max Blumenthal and David Sheen," Beck wrote on his Facebook page with a copy of the letter.
"The two are, on the anniversary of the beginning of the persecution, abduction and murder of more than six million European Jews, presenting a talk that serves anti-Semitic resentments and compares the reign of terror of the Nazis to the Israeli government."
Blumenthal's latest book, Goliath, quotes orthodox Jewish philosopher Yeshayahu Liebowitz's reference to Israeli soldiers as "Judaeo-Nazis".
In the video, Blumenthal is seen saying that Sheen is angry because "he'll have to go to Israel, where he could be - he'll definitely be attacked for these allegations against us."
Blumenthal also says that "Stasi-ism is alive and well" after Gysi, whose political career was born out of the German Democratic Republic, refuses to speak to the pair.
Sheen and Blumenthal, who are both Jewish, say that having their talks cancelled as a precaution against anti-Semitism has branded them as racists against their own people.
They now fear that they will be persecuted because of the statement that was co-signed by Gysi's colleague, Petra Pau.
Blumenthal and Sheen also gave testimony in the German parliament regarding the Israel-Palestine conflict, which they allege Gysi's party also tried to shut down. The parliamentary hearing happened as planned.
On Tuesday evening, Gysi condemned the actions of the journalists in a press statement.
"We won't cooperate with anyone who treats us or our comrades with such hostility like those on November 10," he said.
The three members who invited the two reporters have since apologized to Gysi.
Article clarified at 1300 on 12/11/2014 to show quotes from Max Blumenthal were taken from the linked video.
Article corrected at 1800 on 12/11/2014 to show that Max Blumenthal quoted Yeshayahu Liebowitz in referring to Israeli soldiers as "Judaeo-Nazis"; that Gysi sought to prevent Blumenthal and Sheen speaking at the Bundestag; that Blumenthal has not explicitly compared Israel to the Nazi regime.