As voting got underway the head of the Zambian army warned that violence would not be tolerated and that soldiers would be placed at polling stations to ensure a peaceful election.
General Isaac Shisuze ordered troops to be on alert saying there was information that some people were planning "to cause bloodshed".
"We will not allow them," he said, adding that the army would "deal with anybody who would try to cause violence."
In wrapping up their final rallies the two leading candidates vowed to make economic progress their top goal as the global financial crisis cast a shadow over the polls.
|Sata appealed to the poor with a promise of change and relief from high taxes [AFP]
Banda, a prominent businessman and former diplomat, promised to continue the late president's free market legacy which has made Zambia one of Africa's success stories.
"I will continue the policies and programmes that Mwanawasa started. I will complete them and add more," he told supporters.
He also warned against any disruption to the electoral process, adding: "Until the election results are announced, I am still president and will not allow it."
Mwanawasa's business-friendly policies saw foreign investment in Zambia soar from $71.7m in 2001 to an estimated $4bn in 2008, with $1bn of that coming from China.
The late president won international praise for fighting corruption and modernising the economy, but had admitted failure in lifting the nation out of crushing poverty.
'Vote for change'
Banda's closest rival, Michael Sata, the leader of the opposition Patriotic Front, has portrayed himself as a champion of the poor with a pledge for relief from high taxes.
"You should vote for me so that you can liberate yourselves economically," Sata, popularly known as the "Cobra King", told a rally to chants of "we want change".
Sata has accused Banda's ruling Movement for Multi-Party Democracy of doing too little to create jobs, paying too little attention to rural farmers and pushing taxes too high.
Analysts say Sata's pro-poor rhetoric may be resonating, as prices for copper – the mainstay of Zambia's economy – plummet, while inflation rises and fears of interest rate hikes grow.
About 65 per cent of Zambia's 12 million people live on less than $1 a day.