Santos said that being allied to the popular Uribe did not mean an automatic translation to good election results.
He said he rather expected that "our democracy will be even stronger tomorrow than it is today".
Speaking from Bogota, Lucia Newman, Al Jazeera's Latin America editor, said: "The is an extraordinarily competitive race. One of the most competitive the country has seen in many, many decades."
The ballot is the first round in the election. If neither presidential candidate wins a majority, the elections will go to a second round, with the two top candidates standing in a runoff on June 20.
About 29 million Colombians were eligible to vote.
Al Jazeera's Teresa Bo, reporting from Ciudad Bolivar in Bogota on Sunday, said polling was brisk.
"Many experts were saying that this election was going to have the highest turnout in Colombia's history," she said.
"Generally in Colombia about 40 per cent of the population vote. But experts have said that, this time around, about 50 per cent of the population would cast their ballots."
She said that a proportion of voters typically supporting Santos was focused on security, while another group, generally backing Mockus, gave priority to healthcare and unemployment.
The vote comes amid warnings from the Revolutionary Armed Forces of Colombia (Farc) rebel group that it will try to disrupt the polls.
In response to the threats security has been stepped up across the country, with thousands of soldiers and police on heightened alert in anticipation of possible attacks by Farc.
Santos was a crucial figure in the operation that freed Ingrid Betancourt, a former presidential candidate, and three US security contractors held hostage by the Farc in 2008.
He has relied on Colombia's gains over the leftist rebels under his leadership, arguing he is the best candidate to carry on with Uribe's security policy.
Santos also has portrayed himself as the best candidate to deal with neighbouring Venezuela and Ecuador, both countries with contentious relations with Colombia.
'No to fear'
Santos' campaign rallies have been punctuated by slogans saying "No to fear" in reference to the 46-year-old Farc, responsible for murders, kidnappings and extortion, and general crime as the oldest insurgency in the Americas.
"The Farc intend to interfere in the elections. In some areas of the country they are threatening people to stop them from voting for me," he told his supporters on Saturday.
Former mayor of Bogota and head of Green Party.
Pledges to continue Uribe's security policies but also promises to bring in governmental transparency.
Electoral campaign emphasised economic reforms and tackling high unemployment.
Juan Manuel Santos
Defence minister under Uribe.
Closely involved in the battle against Farc rebels.
His strategies against fighting the Farc have been marred by allegations of human rights abuses.
Also vows to continue Uribe's security policies.
Under Uribe's tenure, military spending increased from three per cent of gross domestic product to 4.1 per cent, boosting the security forces from 220,000 men to 425,000.
Anti-Farc operations over the same period thinned the rebels' ranks from an estimated 17,000 in 2002 to around 7,500.
Mockus, for his part, has also promised to crack down on the rebels though he has also emphasised the economic policies he hopes to implement.
Colombia currently has the highest unemployment rate in South America and Mockus has pledged to create more jobs.
His base of support is the relatively better-off citizenry of the capital, while Santos has aimed his efforts at Colombia's large population of rural and poorer voters.
Gabriel Elizondo, Al Jazeera's correspondent in Colombia's second city, Medellin, said that turnout was very high.
"Here, both Mockus and Santos have a lot of supporters. So both have a lot of reason to get their voters out. But especially Mockus, because so many of his supporters are young and first-time voters," he said.
Our correspondent further said Santos' voters are "probably going to turn up either way ... they are rock solid, middle-aged to older voters. But the younger voters that Mockus is relying on, are the ones that we are simply not sure if they are going to turn out to vote."