A planned airlift of ballot papers and polling officers to remote villages yesterday was disrupted by "extreme thunderstorms" which grounded flights, election authorities said.
Voters in at least two dozen out of around 6,000 polling stations are now expected to cast ballots on Wednesday in a close-fought presidential election to replace Michael Sata, who died in office last year.
In one area, polling material will first have to be transported by boat, then the polling officers will have to walk for three hours before jumping on ox-drawn carts to polling stations, according to the electoral commission.
Fifty-two-year-old Hichilema, a wealthy businessman, is seen as the main challenger to Defence Minister Edgar Lungu, 58, who represents the ruling Patriotic Front (PF).
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"We have no control over the weather," said elections director Priscilla Isaacs.
The head of a Southern African observer team, South African Foreign Minister Maite Nkoana-Mashabane commended the electoral body for holding a "generally peaceful" vote under "challenging" conditions.
Results started to trickle in Wednesday from a handful urban centres, but a final national tally was not expected until Friday.
The vote was triggered after Sata died in October last year from an undisclosed illness.
At stake is the remaining year and a half of his five-year term in the copper-rich southern African nation.
In the absence of reliable opinion polls, analysts hedged their bets.
"It's a two-horse race," said Oliver Saasa, CEO of Premier Consult, a business and economic consultancy firm. "It's quite clear this is a very closely run race."
Hichilema's camp is seen to have received a boost from the infighting within another major opposition party, the Movement for Multiparty Democracy (MMD), whose candidate Nevers Mumba has little chance.
With ideological differences between Zambia's political parties difficult to pin down, voting patterns are often determined by personalities and ethnicity rather than issues.
About 5.2 million people were eligible to vote, but turnout is expected to be low, partly because of the weather.