Khaled Khoja, who was elected early on Monday to head the opposition grouping, said Moscow's proposal was impossible.
"The dialogue with the regime that Moscow is calling for is out of the question," he said at a news conference in Istanbul, where the Coalition is based.
"We can't sit at the same table as the regime... except in a negotiating framework intended to achieve a peaceful transition of power and the formation of a transitional body with full powers," he said.
Russia, a key ally of Syrian President Bashar al-Assad, has been trying to relaunch peace talks that would include meetings between delegates of the regime and the fractured opposition.
It has invited 28 opposition figures, including members of the tolerated domestic opposition as well as individual Coalition members, to Moscow later this month.
Among them are Hadi al-Bahra, whom Khoja succeeded on Monday, and two other previous Coalition chiefs, Moaz al-Khatib and Abdel Basset Sida.
It remains unclear whether the Coalition will seek to ban those of its members who have been invited from attending the talks in Moscow.
'BROTHERHOOD INFLUENCE DECLINING'
Khatib visited Russia last year for discussions and has recently established his own movement, though he remains a member of the Coalition.
Several opposition groups are expected to meet in Cairo this month to form a unified front, according to opposition sources, although a timetable and list of participants has not been made public.
Khoja's comments were the first since he was elected with backing from both secular and moderate Islamist blocs.
He is the first member of the Turkmen minority elected to the post and is seen as more independent than his predecessor, who had strong ties to Saudi Arabia.
Signup to our newsletter and follow us on Facebook and Twitter!
Coalition member Samir Nashar said Khoja's win showed a "decline in the influence of the Muslim Brotherhood", which had backed his rival Nasr Hariri.
Khoja secured 56 votes, six more than Hariri. The election took place in Istanbul.
The National Coalition is the internationally recognised representative of Syria's uprising, but is often accused of being out of touch with reality on the ground in the nearly four-year war.
RIVEN BY CONFLICT
It has also been riven by conflict between its regional backers, including arch-rivals Qatar and Saudi Arabia.
Turkey has also vied for influence, including by backing the Muslim Brotherhood bloc in the coalition.
Khoja has lived in exile in Turkey for decades, after leaving Syria in the 1980s following two stints in prison.
But despite his ties to Turkey, his candidacy was not backed by Ankara.
Nashar, who is close to Khoja, expressed hope that "the new leadership will work to return the Syrian revolution to the right path".
Nashar, who has been critical of Islamist forces in the coalition, also hoped that Khoja would strive to "build a national front committed to the revolution... and establish a pluralist civil state in Syria without exclusion or marginalisation."
Khoja has a history of opposition activism, and was a founding member of the Syrian National Council, a key component of the coalition.
He served as the National Coalition's representative in Turkey before being elected president.
Born in Damascus in 1965, Khoja studied first in Libya after going into exile before settling in Turkey. He graduated in medicine from the University of Izmir in 1994.