In a message, President Kovind said his "thoughts are with the families and individuals who suffered".
"We salute those from the police and security forces who made the supreme sacrifice that day. India remains honour bound to securing justice and defeating terrorism."
He said that the day also marks the 70th anniversary of the adoption of Indian Constitution.
"Let us make the coming year worth this anniversary by giving the Constitutional ethic a greater salience in all our thinking, all our action," the President urged.
"Our solidarity with the bereaved families. A grateful nation bows to our brave police and security forces who valiantly fought the terrorists during the Mumbai attacks," Modi said.
Congress spokesperson Randeep Singh Surjewala said in a message: "Solemnly remembering the 26/11 Mumbai terror attack. My heartfelt gratitude and salutations to the security personnel, bravehearts, NSG commandos, police, firefighters and above all the citizens of Mumbai. Lest We Forget."
Maharashtra Chief Minister Devendra Fadnavis saluted the brave security forces and martyrs who gave a fitting reply to the perpetrators.
"After the attacks, Mumbai's security has been accorded top priority. The city is now under strict CCTV monitoring and we are committed to intensify our war against terror," Fadnavis added, referring to the enhanced efforts to secure the country's commercial capital.
State Congress President Ashok Chavan and former Chief Minister Prithviraj Chavan paid tributes and said "the nation and its people would never forget the extreme sacrifices of their heroes in defending the nation".
State President of Nationalist Congress Party Jayant Patil, Leader of Opposition in Council Dhananjay Munde and other senior leaders like Ajit Pawar visited the 26/11 martyrs memorial at Chowpatty.
Several functions are being held in the city and other parts of the state on Monday to remember the 26/11 carnage and pray for the 166 victims who perished in the 60-hour long attacks carried out by 10 Pakistani terrorists at multiple locations in south Mumbai, shocking the global community.
(With inputs from agencies.)