The announcement comes as Russia and the United States drum up support for their joint initiative to get all parties to the Syrian conflict to join peace talks slated for January 22 in Geneva.
"I have received an invitation from Russian Foreign Minister Sergei Lavrov to visit Moscow delivered by his deputy around 20 days ago," Ahmad Jarba, head of the opposition National Coalition umbrella body, told the official KUNA news agency.
"I have accepted the invitation (but) could not go (yet) because I was busy with other engagements. I will visit Russia to convince them that their interest lies with the Syrian people and not with the regime," said Jarba, who is on his first official visit to Kuwait.
He however gave no date for the visit or any indication whether it would take place before the so-called Geneva 2 peace conference.
Moscow has remained one of the most stubborn supporters of the regime of Syrian President Bashar al-Assad since the Syrian conflict erupted almost 33 months ago.
Jarba said that the National Coalition had decided to attend the Geneva 2 conference under a string of conditions, including that Assad would have no role in Syria's political future.
He added that the opposition conditions, which also included opening humanitarian passages and releasing women and children detainees, were accepted by the friends of Syria meeting held in London and attended by foreign ministers of 11 countries.
"Based on our agreement with the 11 foreign ministers, the Geneva 2 talks will be limited in duration," said Jarba.
"It will lead to a transitional government with real presidential executive powers over security, army, intelligence and the judiciary and Bashar al-Assad will play no role in the transitional period or the future of Syria," Jarba said.
Head of the Syrian National Council, the largest member of the National Coalition, George Sabra said on Sunday that a final decision would taken in mid-December by the Coalition whether it will take part in Geneva 2 talks.
Sabra expressed scepticism that the much-delayed conference would take place as scheduled.
The Geneva talks are aimed at ending the civil war, a bloody stalemate which has killed an estimated 126,000 people and driven millions from their homes.