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Obasanjo, a former military ruler in the 1970s who was also civilian president from 1999 to 2007, told BBC television in an interview that Gnassingbe had to respond to the demands.
“I believe he should have a new constitution that will have a limit to the number of terms that anybody can be president and he should abide by that,” he said on Friday evening.
Obasanjo side-stepped questions about whether Gnassingbe should step down, 12 years after he became president when his father, Gnassingbe Eyadema, died.
Gnassingbe Eyadema ruled the tiny West African nation for nearly 40 years after coming to power following a military coup.
Obasanjo, whose supporters made a failed bid to change the constitution to allow him to seek a third term, questioned whether Faure Gnassingbe still had anything to offer Togo.
“I believe whatever he has to do in terms of development, whatever ideas he has, he must have exhausted them by now, unless he has something new that we don’t know,” he added.
Presidents who were still in office after “12, 15 years, some of them up to 30” were becoming a “rare commodity”, he said.
Two days of anti-government protests this week saw hundreds of thousands of people take to the streets of Togo’s capital, Lome, and other cities across the country.
Opposition supporters are calling for a maximum of two five-year terms for presidents and a switch to a two-round voting system.
The government has proposed a bill on constitutional reform to parliament, which returns for an extraordinary session on Tuesday.
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