Two previous days of unrest in Lome saw violent clashes between security forces and thousands of demonstrators during which stones were thrown, tear gas was fired and about 30 people were injured.
It follows recent electoral reforms ahead of a poll this year.
Protesters want an end to the system allowing unlimited presidential terms.
Togo has been run by the same family for more than four decades.
President Gnassingbe took power in 2005 following the death of his father, Gnassingbe Eyadema, who ruled Togo for 38 years. He was re-elected in 2010.
The BBC’s Ebow Godwin in the capital, Lome, says tens of thousands of people have taken part in the protests.
Anti-riot police fired tear gas at protesters who threw stones, vandalised buildings and set tyres on fire along the capital’s streets.
At least 10 policemen and 17 protesters are thought to have been injured in the previous two days of protest.
The protesters want a reversal of amendments to Togo’s electoral code adopted by the country’s parliament last week, which it says favours the ruling party.
Operation Save Togo, a coalition of campaign groups which organised the protests, said it would continue with the demonstrations until President Faure Gnassingbe agrees to hold a dialogue over the new electoral code and other proposed electoral reforms.
Demonstrators want a return to the Togo 1992 constitution which limits the mandate of a sitting head of state to two terms.
The constitution was amended in 2002 by parliament which was dominated by the ruling party.
Legislative polls are expected to be held in October, however a precise date has not been set.