But Tandja argues that the population wants him to stay.
Tandja cast his vote at a polling station set up in Niamey city hall.
"I have voted, I am fully satisfied that I have done my duty as president of the republic in the face of the demands of the people of Niger," he said.
"It's a great day, our wish has been fulfilled," he added.
State radio urged the population to "go out and vote massively", but turnout appeared low in the first hours of polling, with voters trickling in at several polling stations around the capital.
Not a single voter was in sight at a primary school in the capital's working class suburb of Lazaret just after the polls opened at 8am local time (07:00 GMT).
Two hours later only seven out of 470 voters registered there had bothered to cast their ballots.
"We received the (voting) material on time and opened at 8am, but it's the voters who are not coming out," a returning officer at the station said.
In the lead up to the referendum, Tandja has cracked down on his critics and the press in what his opponents have called a "slow-motion coup".
"I want to ensure that nothing obstructs the sovereign will of the people"
"He took the oath of office swearing on the Quran to protect our nation's democratic institutions," Mahamadou Issoufou, an opposition leader, said.
"But instead, he is destroying them."
Issoufou has called on Niger's estimated six million registered voters to boycott the vote which he called "illegal".
In June, Tandja dissolved the constitutional court that had ruled against him and assumed the power to rule by decree, batting aside international criticism of he move saying he was answerable only to the people of Niger.
The European Union, a major donor to Niger, condemned the move.
"The dissolution of the constitutional court and the exercise of government powers without parliamentary control are grave violations of core democratic values and the principles of the rule of law," Sweden, which holds the revolving presidency of the EU, said.
The European bloc has already suspended the payment of one tranche of aid and warned that the president's pursuit of another term could have "serious consequences" for its co-operation with Niger.
The UN has called for calm during voting.
"The secretary-general calls on the people of Niger to exercise utmost restraint and urges all parties to refrain from any form of violence," said a UN statement.
Security forces, which voted a day ahead of the popular vote, said they would close Niger's borders for 24 hours from midnight on Monday while voting went ahead.
"The government has made provisions to ensure a smooth election to enable every citizen to exercise his right in a calm and secure environment," Tandja said in a television address.
"I want to ensure that nothing obstructs the sovereign will of the people."