"There are allegations of electoral fraud," Chadema spokesman Tumaini Makene told reporters late Sunday.
John Magufuli of the long-ruling Chama Cha Mapinduzi (CCM) is seen as the narrow favourite to beat ex-Prime Minister Edward Lowassa, a CCM stalwart who recently defected to Chadema, which is heading a coalition of opposition parties.
But analysts have warned that the unusually tight race could spark tensions, with the opposition providing the first credible challenge to the CCM since the introduction of multi-party democracy in 1995.
While voting passed off largely peacefully, senior Chadema official Mwesiga Baregu told reporters they were concerned at reports of "a number of reported interceptions of stuffed [ballot] boxes."
The opposition claims could not be independently verified, but Chadema said it was concerned.
"We seem to be heading to results that may not be credible, and therefore might not be accepted not just by political parties, but will not be accepted by the voters themselves," Baregu said.
Election officials said they expect the results of the presidential race within three days, but some early results are expected to begin arriving today.
Many believe 55-year old Magufuli currently minister of works, for which he earned the nickname "The Bulldozer" will face a tough challenge from Lowassa, 62.
Lowassa was prime minister from 2005 until his resignation in 2008 over corruption allegations that he denies, and has for years been a CCM loyalist, but on the campaign trail he called for an end to the party`s rule.
Outgoing President Jakaya Kikwete, who is not running having served his constitutional two-term limit, ordered the police to boost security to ensure calm in the country of 52 million people, of whom 22 million are registered to vote.
As well as a presidential race, voters also cast ballots in parliamentary and local polls on Sunday, including on the semi-autonomous archipelago of Zanzibar, just off mainland Tanzania, which was holding its own presidential elections.
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