UPDATE 4-Brazil's largest cities hit by blackout

* Blackout hits Sao Paulo and Rio de Janeiro

* Fault in transmission grid is suspected cause

* At least six Brazilian states are affected

* Neighboring Paraguay also suffers power loss (Recasts with problem blamed on transmission lines)

By Bruno Marfinati

SAO PAULO, Nov 10 (Reuters - A major electricity outage left tens of millions of people in Brazil's two biggest cities without power on Tuesday night due to problems with the transmission lines that connect to the massive Itaipu dam.

The blackout affected Sao Paulo and Rio de Janeiro, as well as cities in at least four other states, hitting the industrialized southeastern part of Latin America's largest country especially hard.

All of Paraguay, which gets most of its energy from the dam, was also briefly left in the dark.

Three hours after the blackout, power was beginning to be restored in some parts of Sao Paulo, Brazil's financial capital and South America's largest city. But much of the sprawling metropolis remained in the dark.