Speaking at a summit in Bissau after being named chairman of the Economic Community of West African States (ECOWAS), Tinubu said democracy was "the best form of government", despite being "very tough to manage".
"We need it, to be an example to the rest of Africa and the world," he said. "We will not allow coup after coup in West Africa."
Three ECOWAS members – Mali, Guinea and Burkina Faso – have undergone five putsches since 2020.
Omar Alieu Touray, president of the ECOWAS commission, urged those countries' ruling juntas to respect agreed-upon deadlines to hand power to civilian leaders.
"In the event of a failure to meet the transition deadlines, major sanctions could be imposed," he said.
The West African Economic and Monetary Union (UEMOA) on Saturday agreed to lift a suspension of Mali imposed in January 2022 over the military's timeline for returning to civilian rule.
ECOWAS had also imposed a range of measures against the Sahel state, but lifted them in July 2022 after the junta agreed to a March 2024 transition.
On Sunday, Touray said ECOWAS had set up a commission to examine security options in Mali as the UN winds down its decade-long peacekeeping mission there.
"This commission has 90 days to reflect and make proposals," he said.
Mali has since 2012 been battling a jihadist insurgency that has since spread to Burkina Faso and Niger.
Tinubu – who was in May sworn in as president of Africa's largest economy – said ECOWAS members would pursue "inclusive" economic integration in the year ahead.
"We should serve a warning to exploiters that our people have suffered enough," he said on Sunday.
"I am with you – and Nigeria, we are back."
