Protesters in Venezuela have accused the government of murdering a jailed opposition lawmaker who the authorities say killed himself.
But his supporters say he was murdered - a theory echoed by the United States, a fierce critic of Maduro's regime.
The Venezuelan government and the opposition have also disputed the reasons behind Alban's arrest.
"Alban requested to go to the bathroom and jumped from there", said Saab to the Venezuelan state television (VTV), adding that an "exhaustive investigation" will be conducted to "determine and establish the causes of this unfortunate event".
He represented a district in the Caracas area.
Borges, who led the delegation to the United Nations, said Alban's wife told him that her husband had been under intense pressure to testify against him in the ongoing probe into the alleged plot in early August to kill Maduro using two drones loaded with explosives.
Borges said that as a deep Catholic and family man Salazar would never consider killing himself.
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He was in the USA accompanying other members of his First Justice party for meetings with foreign dignitaries attending the United Nations General Assembly. On Monday, Reverol said Alban had also been investigated for "destabilising activities directed from overseas".
Republican Sen. Bob Corker, the outgoing chairman of the Senate Foreign Relations Committee, who is in Venezuela for meetings with Maduro and his opponents, called Alban's death while in the government's custody "disturbing". "We understand there are conflicting reports on what exactly happened".
Maduro was unharmed but several members of the military sustained injuries.
Rights groups and the opposition have said that Mr Maduro's administration is holding hundreds of political prisoners on trumped-up charges meant to stifle dissent. The United Nations has said detainees are often subjected to ill treatment, including some documented cases that amount to torture. He said Mr Alban told him that he had been interrogated, but not tortured. The government denies they are political prisoners.
Alban's lawyer, Joel Garcia, told reporters that when he last saw Alban on Sunday "he was not beaten, he was fine".
While dozens of youths were killed in violent street battles with security forces past year, the death of government opponents while in state custody came as a shock to many Venezuelans, something akin to the far deadlier, right-wing dictatorships that dominated South America in the 1970s that Maduro frequently denounces.
The Organization of American States (OAS), a group of Western hemisphere countries, has condemned Alban's death.