Police in Togo have fired tear gas in an effort to disperse hundreds of opposition supporters who took to the streets of the capital, Lome.
Mr Faure quit after intense pressure from African neighbours
The police intervened after protesters gathered on main roads close to the Be area, an opposition stronghold.
The violence came two days after Faure Gnassingbe, the late president's son, agreed to step down as Togo's leader.
The protesters, who threw stones and tried to erect barricades, said the constitution was still being violated.
They called for former parliamentary speaker Fambare Ouattara Natchaba to take over as interim president, in accordance with constitutional procedures.
The demonstrators rejected the appointment of Abass Bonfoh, who became acting president late on Friday when the national assembly named him as its new speaker in the wake of Mr Faure's resignation.
Togo was plunged into crisis earlier this month after Mr Faure was installed as president by the army, hours after the death of his father, Gnassingbe Eyadema.
Although he promised elections within 60 days, as stipulated by the constitution, this did little to quell protests from African neighbours and beyond.
But on Friday, he said he was stepping down because he wanted to ensure the transparency of the election, now due in April, in which he plans to stand as a candidate.
On Saturday, the West African regional grouping Ecowas said it was lifting sanctions against Togo with immediate effect.
UN Secretary General Kofi Annan welcomed Mr Faure's decision, while a spokeswoman for Nigerian President Olesegun Obasanjo, who chairs the African Union, described it as a "victory for democracy".
Constitutional amendments swiftly introduced to legitimise Mr Faure's appointment have since been partly reversed.