(CNN) -- Liberia went to the polls Tuesday for a runoff election after incumbent President Ellen Johnson Sirleaf failed to win the votes needed for an outright victory last month.
Johnson Sirleaf, who won the Nobel Peace Prize this year, needed 50% to avoid a runoff in the October 11 election, but did not reach it. Polls were scheduled to close at 1 p.m. EST.
She faces challenger Winston Tubman, who came second.
While the U.S.-based Carter Center said the October balloting was "peaceful, orderly, and remarkably transparent," opposition parties have protested the results, and claimed voting irregularities.
Tubman has reportedly refused to participate in the runoff, alleging it won't be fair, and there have been calls to boycott the election, the United Nations has said.
On Monday, members of the Tubman's Congress for Democratic Change clashed with police in what authorities called an unauthorized protest, state-owned radio network Liberia Broadcasting System reported.
At least one person was killed and several others wounded in the clashes in the capital city of Monrovia, the network reported.
Both U.N. Secretary-General Ban Ki-moon and the Security Council have called on Liberians to refrain from violence.
"Regardless of your political views, I appeal to all Liberians to say no to violence on Election Day," said Ellen Margrethe Loj, the U.N.Secretary-General's special representative and head of the U.N. Mission in Liberia (UNMIL).
It is the second presidential election since a 14-year civil war ended in 2005.
The war devastated Liberia and left an estimated 250,000 people dead, and voters are hoping for more peaceful and prosperous days ahead.
Johnson Sirleaf has said she wants to preserve the peace.
"We've put in the fundamentals, the foundation -- the possibility to reach our accelerated growth and development, fix our infrastructure, the potential, and chances are so high," she said before the election.
Liberia faces many challenges: up to 80% of Liberians are unemployed and a majority live without basic necessities such as water and electricity.