HNC coordinator Riyad Hijab is said to have "received a personal invitation" to attend Friday's talks "but declined".
High Negotiations Committee spokesman Riyad Naasan said that HNC coordinator Riyad Hijab had "received a personal invitation" to attend Friday's talks "but declined".
But "no invitation has yet been sent to the High Negotiations Committee", he added.
The HNC is the main Syrian opposition umbrella group and has taken part in peace talks brokered by Syria regime allies Russia and Iran and rebel backer Turkey in the Kazakh capital, Astana, this week.
The Turkey-based opposition National Coalition also declined to meet with Lavrov, said spokesman Ahmad Ramadan.
He said invitations were sent to the current and past heads of the National Coalition and to the deputy of the sitting chief.
On Wednesday Lavrov told Russian lawmakers that he had invited "all the opposition representatives from the political opposition that wish to come to Moscow" for talks on Friday.
He said "we will brief them about what happened in Astana".
The peace talks in the Kazakh capital ended on Tuesday without a major breakthrough.
A spokeswoman for the Russian foreign ministry did not name which Syrian opposition groups had been invited to meet with Lavrov.
Syria's opposition comprises a wide range of factions, including moderate rebels and Islamist armed groups, and only non-jihadists attended the Astana talks.
Russia, Iran and Turkey agreed in Astana to establish a joint "mechanism" to shore up a shaky three-week truce in Syria, but offered few concrete details on how it would work.