The region has been beset by a series of political crises and Tinubu told heads of state gathered for the ECOWAS talks in Nigeria's capital that they were meeting at a "critical juncture."
"I come before you today burdened by the weight of the challenges confronting us," said Tinubu, who is also head of the Economic Community of West African States, ECOWAS, regional bloc.
Following recent coups in Mali, Burkina Faso, Niger and Guinea, Tinubu said "we must re-examine our current approach to the quest for constitutional order in four of our members’ states."
The four have been suspended from the organization and were not represented at the summit.
Mali, Burkina Faso and Niger declared their intention to permanently withdraw from the bloc in January, but ECOWAS has called for them to return.
Tinubu urged them to "reconsider the decision" and said they should "not perceive our organization as the enemy."
The three countries' new military leaders have accused former colonial power France of instrumentalizing ECOWAS, and they have pushed out French ambassadors and forces while turning politically and militarily toward Russia.
Tinubu was set to give a statement about the bloc's discussions later in the day after private talks between leaders.
Niger was expected to be a main focus, with the organization saying before the meeting it would concentrate on politics and security in the country.
Niger's President Mohamed Bazoum was ousted in a military coup last July, prompting ECOWAS to suspend trade and impose tough sanctions.
But the bloc's warning of military intervention has fizzled out with little sign that Bazoum – still imprisoned in the presidential palace in Niamey – is closer to being restored.
On the eve of the summit lawyers for Bazoum urged ECOWAS to demand his release.
Earlier this week, ECOWAS co-founder and former Nigerian military leader General Yakubu Gowon called for the body to lift "all sanctions that have been imposed on Burkina Faso, Guinea, Mali and Niger."
West Africa has also been rattled by President Macky Sall's sudden decision to delay elections in Senegal.
Sall has faced growing calls to set a date for the presidential election after his postponement of the February 25 poll triggered weeks of turmoil. He has stressed his mandate will end as planned on April 2.
Sall attended Saturday's summit, but it was not clear if the leaders would discuss the crisis in Senegal.
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