The Economic Community of West African States, ECOWAS said in a statement on social media that it "encourages the political class to take steps urgently to restore the electoral calendar".
The regional body said it was following the unfolding events in Senegal “with concern”.
ECOWAS also called on all parties "to shun violence and all other actions that may further disturb the peace and stability of the country".
"It urges the law enforcement agencies to exercise utmost restraint and protect the fundamental rights of all citizens," the statement added.
Senegal’s parliament late on Monday voted to postpone the polls and for President Macky Sall to remain in office until his successor is installed.