Pro-Kremlin candidates have suffered major losses in a Moscow municipal election following an opposition-led strategic voting campaign, Russian news agencies have reported.

With nearly all votes counted, news agencies reported significant gains for independent, Communist and liberal candidates against those allied with the ruling United Russia party.

The Communists were on track to win 13 or 14 seats, up from only five in the previous assembly, Interfax and RIA Novosti reported.

The liberal Yabloko party and left-leaning Just Russia party were set to take three seats each, after having none previously.

Pro-Kremlin deputies held 38 of the assembly's 45 seats after the previous election in 2014, with 28 belonging to United Russia.

No candidates ran under its banner this year as the party is deeply unpopular.

Interfax said nine previous deputies of United Russia had retained their seats but that the party's leader in Moscow Andrei Metelsky, had lost a re-election bid.

After his allies were banned from the vote, main opposition leader Alexei Navalny put forward a "Smart Voting" plan urging Muscovites to support those who had the highest chances of beating pro-Kremlin candidates.