An interview with the late grandmother of Donald Trump’s son-in-law and close aide Jared Kushner has re-emerged in which she describes her anguish over America’s refusal to accept Jews fleeing the Holocaust.

The rediscovery of the video comes amid an international furore over the US president’s executive order denying entry to citizens of seven Muslim countries.

Excerpts from the transcript of the interview with Rae Kushner, taped in 1982 and published in the US Holocaust Memorial Museum in Washington, have been reported in several Israeli newspapers this week and contain parallels with the situation faced by refugees today.

Rae Kushner was one of the only members of her family to survive the second world war. She talks about the difficulties she faced as a Nazi-era Jewish refugee and criticises the US – beset by an anti-immigrant sentiment at the time – for its reluctance to take people in.

She was born in 1923 in Novogrudok, a city then in Poland and occupied first by the Soviet Union and then the Nazis, who turned it into a Jewish ghetto. Kushner managed to escape with her father and sister through a tunnel, before living in woods for nine months, then smuggling themselves over several borders, ending up in a refugee camp in Italy. Kushner lived there for three and a half years until relatives in the US helped to get visas for her and her husband Joseph, whom she had met in Hungary.

“A few Jews, friends of my father’s who had stores, left everything and went to Palestine. [Even before the war] they said to my father and mother, ‘Sell everything and run,’ ” Kushner said.

“But we had a problem. We didn’t know where to run. There was no Israel like there is today. There was no place that you could legally go to. It was very hard to get a visa to the United States; it would take years and years.

“For a family with small kids to pick themselves up and go it was very hard. But a few families left to Palestine and they stayed alive. We felt the antisemitism. We felt something was coming, but we couldn’t help ourselves.

“The doors of the world were closed to us. You know how hard it was to get to Israel? Boys and girls used to sit in a camp for three or four years before they could go to Palestine. To go to America was harder. You sent your papers and you waited for years before you could get a visa.”

Kushner also recalled how in 1941 she had been one of 50 girls taken by the Germans to the town square in Novogrudok and asked to wash blood from the stones where the Nazis had just executed scores of intellectuals.

“The German shot them as [a band] was playing,” she said. “We put the dead bodies on a wagon. The heads of the people were hanging off the back of the wagon.”

A group including Holocaust survivors enter Auschwitz-Birkenau in Poland on 27 January to mark the 72nd anniversary of its liberation by Soviet troops. Photograph: Agencja Gazeta/Reuters

Kushner’s account of her arduous journey through an unwelcoming Europe reads like some of the accounts given by Syrians fleeing war today.

“We got off the train in Czechoslovakia,” she said. “The borders were all closed to us. So we got off the train and hid until it was dark. We then walked into the hills and smuggled through the borders. We would walk all night long and rest during the day. We walked from Czechoslovakia to Austria and then to Hungary. I met my husband in Hungary and we got married.

“We then crossed the border again to Italy. We did this all on foot, all in the middle of the night so that no one would see us. We came to Italy where there were two displaced persons camps. One was in Cremona and the other one was in Ladispoli. We were put up in Cremona where we waited for three and a half years before getting papers for America.”

Reflecting on the Holocaust later in the interview, Kushner lamented the harsh US policy towards Jewish refugees, especially those on board the St Louis, a refugee ship turned back by the US in 1939.

“For the Jews, the doors were closed. We never understood that. Even President Roosevelt kept the doors closed. Why? The boat, St. Louis, was turned back. What was the world afraid of? I don’t understand.”

A Twitter account launched last week on Holocaust Memorial Day has detailed the fate of the Jews on the St Louis manifest, many of whom were murdered by the Nazis and their allies on their return to Europe.

The US rejection of Jewish refugees from Europe during the Nazi rise to power and as war got under way reflected a widespread populist xenophobia and anti-immigrant sentiment aimed at Jews, Catholics and others. Jared Kushner has faced criticism – including in a scathing comment piece this week in the Israeli newspaper Haaretz – for deploying his family’s experience of the Holocaust during the election campaign to defend Trump and his entourage against accusations of antisemitism.

Allison Kaplan Sommer, a Hareetz columnist, directly linked Jared Kushner’s support for Trump with the president’s ban and Rae’s experiences. “Since it was Kushner himself who brought his family’s Holocaust legacy into the political fray, it feels fair to force him to confront the way in which he is now party to inflicting his grandmother’s suffering on others.”