The Obama administration's international surveillance crisis deepened on Monday as representatives from a Latin American human rights panel told US diplomats that oversight of the programs was "illusory".

Members of the Inter-American Commission on Human Rights, an arm of the Organization of American States, expressed frustration and dissatisfaction with the National Security Agency's mass surveillance of foreign nationals – something the agency argues is both central to its existence and necessary to prevent terrorism.

"With a program of this scope, it's obvious that any form of control becomes illusory when there's hundreds of millions of communications that become monitored and surveilled," said Felipe Gonzales, a commissioner and Chilean national.

"This is of concern to us because maybe the Inter-American Committee on Human Rights may become a target as well of surveillance," said Rodrigo Escobar Gil, a commissioner and Colombian citizen.

Frank La Rue, the United Nations special rapporteur on the right to freedom of opinion and expression, told the commission that the right to privacy was "inextricably linked" to free expression.

"What is not permissible from a human rights point of view is that those that hold political power or those that are in security agencies or, even less, those in intelligence agencies decide by themselves, for themselves, what the scope of these surveillance activities are, or who will be targeted, or who will be blank surveilled," La Rue said.

While the US sent four representatives to the hearing, they offered no defence, rebuttal or elaboration about bulk surveillance, saying the October government shutdown prevented them from adequate preparation. "We are here to listen," said deputy permanent representative Lawrence Gumbiner, who pledged to submit written responses within 30 days.

All 35 North, Central and South American nations are members of the commission. La Rue, originally from Guatemala and an independent expert appointed by the Human Rights Council, travels the world reporting on human rights concerns – often in countries with poor democratic standards.

Spying on foreigners is the core mission of the NSA, one that it vigorously defends as appropriate, legal and unexceptional given the nature of global threats and widespread spycraft. Monday's hearing suggested that there are diplomatic consequences to bulk surveillance even if there may not be legal redress for non-Americans.

Brazil has already shown a willingness to challenge Washington over bulk surveillance. President Dilma Rousseff postponed a September meeting with President Obama in protest, and denounced the spying during the UN general assembly shortly thereafter. Brazil is also teaming up with Germany at the UN on a general assembly resolution demanding an end to the mass surveillance.

The commission's examination of the NSA's bulk surveillance activities suggested a potential southern front could open in the spy crisis just as the administration is attempting to calm down Europe.

The Obama administration has been fielding a week's worth of European outrage following media reports that the NSA had collected a similarly large volume of phone calls from France – which director of national intelligence James Clapper, who recently apologised for misleading the Senate about domestic spying, called "false" – and spying on German chancellor Angela Merkel's own cellphone, which US officials have effectively confessed to.

Brazil and Mexico are also demanding answers from US intelligence officials, following reports about intrusive acts of espionage in their territory revealed by documents provided to journalists by former NSA contractor Edward Snowden. The White House has said it will provide some answers after the completion of an external review of its surveillance programs, scheduled to be completed before the end of the year.

The Guardian reported on Thursday that the NSA has intercepted the communications of 35 world leaders.

International discomfort with NSA bulk surveillance is not the only spy challenge the Obama administration now confronts.

Congressman James Sensenbrenner, the Wisconsin Republican and key author of the 2001 Patriot Act, is poised to introduce a bill this week that would prevent the NSA from collecting phone records on American citizens in bulk and without an individual warrant. The National Journal reported that Sensenbrenner's bill, which has a companion in the Senate, has attracted eight co-sponsors who either voted against or abstained on a July amendment in the House that would have defunded the domestic phone records bulk collection, a legislative gambit that came within seven votes of passage.

Sensenbrenner's bill, like its Senate counterpart sponsored by Vermont Democrat Patrick Leahy, would not substantially restrict the NSA's foreign-focused surveillance, which is a traditional NSA activity. There is practically no congressional appetite, and no viable legislation, to limit the NSA from intercepting the communications of foreigners.

An early sign about the course of potential surveillance reforms in the House of Representatives may come as early as Tuesday. The House intelligence committee, a hotbed of support for the NSA, will hold its first public hearing of the fall legislative calendar on proposed surveillance legislation. Its chairman, Mike Rogers of Michigan, has proposed requiring greater transparency on the NSA and the surveillance court that oversees it, but would largely leave the actual surveillance activities of the NSA, inside and outside the United States, untouched.

Alex Abdo, a lawyer with the ACLU, which requested the hearing at the Inter-American Commission on Human Rights, warned the human rights panel that the NSA could "target the foreign members of this commission when they travel abroad", as well as foreign dissidents of US-aligned governments; foreign lawyers for Guantánamo detainees; and other foreigners.

"If every country were to engage in surveillance as pervasive as the NSA, we would soon live in a state … with no refuge for the world's dissidents, journalists and human rights defenders," Abdo said.