Keita, 73, is running against Soumalia Cisse, 68, the main opposition leader and a former finance minister.
The first round on July 29 was marred by armed attacks and other security incidents at about a fifth of polling places, as well as opposition charges of fraud.
As voting progressed throughout Sunday, however, no serious incidents had been reported. Soldiers ran body checks on voters in the capital Bamako as they waited in line under rainy skies to cast their ballots.
Dramane Camara, 31, was the first to vote at one polling station in a school in the capital Bamako.
“I voted without problem, I came to fulfil my duty as a citizen,” Camara said. “I expect the new president to solve the problem of the North, which is peace. Because the return of peace means the return of NGOs, investors, so creating jobs.”
The chaotic first round was a reminder that militants, some linked to al Qaeda and Islamic State, have regrouped since French troops intervened in 2013 to push them back from areas they had seized in Mali’s desert north.
They are now expanding their influence again across the north and into the fertile centre.
Their presence in the vast West African nation and their ability to spread violence to its neighbours has kept Mali high on the list of Western powers’ security concerns. Former colonial ruler France and the United States have deployed thousands of troops across the region.
Keita called for a peaceful day and urged people not to respond to any provocation as he voted in Bamako on Sunday morning. “I pledge that all the difficulties we faced are now behind us,” he told cheering supporters.
The government has stepped up security for the run-off, deploying an extra 6,000 troops on top of the 30,000 already on duty. The Mopti region in central Mali, where most of the attacks in the first round took place, is a particular concern.
The head of the European Union observer mission, Italian politician Cecile Kyenge, told reporters there had been no major incidents at 40 polling stations it had monitored. She added that 95 percent of them had opened on time.
The mission had deployed 90 observers across the country “but unfortunately not to Timbuktu, Mopti and Kidal” — areas where violence has been rife.
Keita took 41 percent of the vote in last month’s first round against nearly 18 percent for Cisse.
Cisse, who lost against Keita before in a peaceful 2013 run-off, accused Keita’s government of voting fraud in the first round this time but the constitutional court upheld the result.
Cisse blames Keita for the worsening violence and accuses his government of rampant corruption. Civil society website Malilink recorded 932 militant attacks in the first half of 2018, almost double that for all of 2017.
Jihadists are also stoking inter-communal conflict, mostly between herders and traditional hunters. Killings along ethnic lines have claimed hundreds of civilian lives this year, including at least 11 last week in the Mopti region.
Keita’s better-than-expected first-round showing and Cisse’s failure to win endorsements from the third and fourth-place finishers augur well for the incumbent to secure another five-year term. Results from the first round took five days to emerge and authorities have not said when they expect the final result to be announced.
At his final rally in the capital Bamako on Friday, Keita — known as IBK — struck a confident tone.
“Some people were sceptical that these elections could take place. Some called on me to withdraw,” he said above the din of his supporters’ vuvuzelas. “Let them understand that we had the capacity to organise credible elections and we have done so.”
On Saturday evening, about 100 opposition supporters demonstrated in Bamako’s Liberty Square to complain about the result of the first round. Chanting “No to electoral fraud” and calling for transparency in the second round, they said there had been many instances of cheating in the first vote.
Armed troops watched over the protest but did not intervene.
Despite the militant threat, Malian polls have generally gone peacefully without the post-election violence common to many countries in the region. The 2013 elections followed a military coup a year earlier.
Fatoumata Cissé, a 38-year-old teacher, said: “I voted, no problem. I voted IBK. He has a positive balance especially for us teachers, our living conditions have improved. I hope that it will continue to improve the conditions of workers.”