The demonstrators are seeking for a two-term presidential tenure, and asking the incumbent president to leave office.
Faure became president after the death of his father Gnassingbé Eyadema, who ruled Togo for 38 years. The protesters are asking the current president to step down after having been in power since 2005.
The demonstrations held across many cities by a coalition of opposition parties and civil organizations have been met by stiff resistance by the police, with some said to have been arrested, charged and sentenced after similar protests the previous week.
In August, two opposition protesters were killed and 13 others wounded when security forces opened fire to break up demonstrations.
They chanted: "50 years is too long".
The protesters have said they won’t stop until their push for a two-term presidential limit was met.
One demonstrator, Luc Koffi, told AFP that he wants the president to step down:
"We suffer too much, we can't even find food. What country are we in? We don't want Faure any more, he must go," he said.
A decision by the cabinet to propose a constitutional change to bring about a presidential term-limit has not changed the protesters' plans.
They see it as part of a trick to extend Mr Gnassingbé's rule.
Internet speeds have been restricted, Facebook and Whatsapp access had been limited.
Though mobile internet has been shut down in the capital, Lome, wi-fi networks are said to still be working.
On Twitter, some activists said they were headed to the Ghanaian border to use the country’s internet and voice their criticism of Gnassingbé.
Government spokesperson, Gilbert Bawara, told a local radio station that there was an ongoing internet restriction.
"Even in most developed countries, authorities take control of telecommunications in some cases," he said.
Last year as many as 11 African countries shut down internet access ahead of elections and anti-government protests.
In Gabon and The Gambia, internet was shut down during and after elections as well as in Ethiopia and The Democratic Republic of Congo.
Earlier in 2017, Cameroon imposed a 93-day internet blackout on the country's Anglophone regions which spoke out on being marginalized by the French-speaking government. The blackout lasted 93 days despite international criticism.