The envoy, Senegalese diplomat Abdoulaye Bathily, had on Monday told the United Nations Security Council he planned to create a "high-level steering panel" to enable presidential and legislative elections to be held this year.
Legislative and presidential polls had been set for December 2021 but were postponed indefinitely amid bitter divisions over who could stand and what powers the president would have, among other issues.
Bathily noted that the eastern-based parliament and Libya's High Council of State, based in Tripoli, had "not been able to agree on a consensual constitutional basis for elections."
In a statement on Tuesday, the office of parliament chief Aguila Saleh voiced "surprise at the errors in the briefing over the failure of parliament and the HCS to agree a constitutional basis for elections."
The statement accused Bathily of "double standards" and "lacking impartiality."
The form and rules around elections have been key sticking points in Libya's faltering peace process since the last major round of fighting in the North African country, torn apart by a decade of war.
Saleh's House of Representatives earlier this month passed an amendment to the country's Constitutional Declaration - an interim constitution- which it said would provide a legal basis for elections.
In his briefing, Bathily noted that the amendment had "yet to be endorsed" by the HCS.
The "amendment is controversial within the Libyan political class and general citizenry", he added.
"It does not address key contentious issues such as the eligibility criteria for presidential candidates (and) does not stipulate a clear road map."
Libya has been riven by conflict since the 2011 revolt that toppled and killed dictator Moamer Kadhafi.
Two rival administrations are vying for power, that of interim prime minister Abdelhamid Dbeibah in the western capital, Tripoli, and a separate government in the central city of Sirte, backed by the eastern-based parliament.