This measure announced on Wednesday was part of two declarations signed by President Donald Trump, reports Efe news
The first ban, which affected the South American nation, was imposed on "members of the regime of Nicolas Maduro" at the level of Deputy Minister, or equivalent, and above.
The restriction was announced shortly before Venezuelan Vice President Delcy Rodriguez was set to depart for New York City to address the UN General Assembly (UNGA) on behalf of her country.
A senior US official told Efe news that "the proclamation doesn't affect the US government's obligations under applicable international treaties".
As the host country of the UN, the US is required to facilitate foreign officials' travel to the headquarters of the international organization.
The Venezuelan delegation to the UNGA also included Venezuelan Foreign Minister Jorge Arreaza, who was already in New York participating in various meetings.
Trump's proclamation prohibits the entry into the US of all members of the National Constituent Assembly - a parallel legislative counter to the opposition-controlled National Assembly that is fully occupied by pro-Maduro lawmakers - and "all officers of the Venezuelan military, police, or national guard at the rank of colonel, or equivalent, and above".
The measure also affects any foreigner who acts "on behalf of or in support of the Maduro regime's efforts to undermine or injure Venezuela's democratic institutions," as well as aliens who obtain "significant financial benefit" from transactions or business dealings with the Venezuelan authorities.
The prohibition extends to the immediate family members of the sanctioned individuals.
In the case of Iran, the ban applies to senior government officials and their immediate families.
Iranian President Hassan Rouhani is currently in New York, where he addressed the UNGA on Wednesday and plans to hold a press conference on Thursday morning.
Foreign Minister Mohammad Javad Zarif is also currently in New York.
Before leaving Tehran, the Iranian delegation warned of the possibility of cancelling their trip because US authorities were showing a delay in granting the required visas.
The proclamations signed by Trump give the Secretary of State the authority to allow the entry of some of these individuals if it is considered that their travel would not harm the US interests.
At a press conference in New York, Trump mentioned the issue in passing during a review of the actions his administration is taking against what it describes as the "dictatorships" of Venezuela and Iran.
Both countries have already been the recipients of broad diplomatic and economic sanctions following a US-led diplomatic blitz.
( With inputs from IANS )