Tubman is boycotting Tuesday's balloting, alleging voter fraud in the first round. His supporters clashed with police Monday outside the headquarters of Tubman's Congress for Democratic Change party. At least one person was killed, the Voice of America reported Tuesday.
Election observers, who said the first round of voting was generally free and fair, said voter turnout appears to be low.
The incumbent president, a Nobel Peace laureate, defeated Tubman in the first round, 44 to 32 percent, but failed to get the 50 percent majority required for an outright victory.
U.N. Secretary-General Ban Ki-moon has urged the people of Liberia to refrain from violence despite their political disagreements.
"The secretary-general stresses the importance of peaceful, credible, transparent elections and reaffirms the readiness of the United Nations Mission in Liberia to support the Liberian authorities, in accordance with its mandate," a spokesman for the U.N. leader said.