D'Escoto's spokesman later said that the threats were not related to criticism he had voiced against Israel.
Ambassador Shalev was on her way to meet with D'Escoto as per his request, when she was informed that half an hour earlier the Nicaraguan head of the General Assembly had issued a press release including harsh accusations against Israel.
D'Escoto, a Catholic priest, has repeatedly criticized both the United States and Israel since taking office in September. Recently he compared Israel's treatment of the Palestinians to the former South African apartheid racial segregation policy.
The recent argument for D'Escoto's statement was linked to Israel's refusal to allow a special UN officer, who planned to travel to the Palestinian territories to document human rights conditions, to enter Israel.
Border police prevented Richard Falk, the UN Special Rapporteur on Israeli conduct in the West Bank and Gaza Strip, from entering Israel when he arrived at Ben-Gurion Airport near Tel Aviv on Sunday.
Falk had angered Israel by making remarks comparing its forces' actions in the Gaza Strip to those of the Nazis in wartime Europe. He was put on a plane back to Geneva on Monday.
UN officials said Falk, who is Jewish, has been tasked with preparing reports on human rights violations in the West Bank and Gaza Strip. "He was coming to follow up on his mandate, meet people and collect first-hand information," a UN official said.
A US professor, Falk is fiercely critical of what he describes as "pro-Israel" influence on US foreign policies.
Yigal Palmor, an Israeli Foreign Ministry spokesman, said Falk was denied entry because his mandate from the UN's Human Rights Council was "profoundly distorted and conceived as an anti-Israel initiative".
"It has nothing to do with the promotion of human rights," Palmor said, noting that Falk's mandate allows him to report only on Israeli violations of human rights and international humanitarian law in the territories.
Sources at the UN delegation in New York said Falk was banned entry because he did present a diplomatic passport.
'D'Escoto abusing his position'
Following the incident, D'Escoto issued a statement calling Israel's treatment of Falk 'arbitrary'.
Such an action by a country which country which is a member of the UN reflects a dangerous decision by individual countries to rebuff UN mandates, he said.
Israel was angered by the criticism, particularly as Falk, who came from Geneva, is not linked in any way to the UN headquarters in New York or to D'Escoto. Ambassador Shalev sought to explain to the General Assembly head why Falk was refused entry, but D'Escoto's recent statement infuriated her.
Mirit Cohen, spokeswoman for Israel's mission to the United Nations, described the statement as "outrageous" and said Shalev canceled a planned meeting with D'Escoto because of it.
"The role of the president of the General Assembly should be to unite the international community and promote shared interests and values," Cohen said. "However, since his first days as president of the General Assembly, Mr. D'Escoto has been divisive and controversial, abusing his position."
"This matter is being looked into by the pertinent authorities. They are very serious threats against his life and he is taking it pretty seriously," he told reporters. "Also the security staff at the UN is taking it very seriously."
Reuters contributed to this report