The presidential election is seen as a test of Liberia’s fragile democracy after 14 years of vicious civil war.
“We will never reward fraud and abuse of power and will never grant legitimacy to a corrupt political process,” Mr Tubman told reporters in Monrovia.
He called for a peaceful protest on Saturday and for his supporters to boycott next week’s vote.
The new head of Liberia’s election commission, Elizabeth Nelson, said the presidential vote would go ahead as planned.
The West African regional body Ecowas has warned that a boycott risks destabilising Liberia and called on Mr Tubman not to pull out of the process.
The former head of the election commission, James Fromayan, resigned last week after Mr Tubman’s CDC complained it was biased.
But the party had said other checks and balances had to be put in place for Mr Tubman to take part in the vote.
In the presidential run-off, Mr Tubman would have faced Nobel Peace laureate Ellen Johnson-Sirleaf.
She became Africa’s first female elected head of state after the 2005 elections following the end of Liberia’s 14-year civil war in which 250,000 people were killed.
Mr Tubman’s Congress for Democratic Change (CDC) party alleged widespread fraud in last month’s first round, but international observers said the polls had been peaceful and transparent.
These are the first post-war elections organised by Liberians – the previous poll was run by the UN, which still has some 8,000 peacekeepers in the country.
Mrs Sirleaf gained 44% against 32% for Mr Tubman. A candidate needs most than 50% for outright victory.
Mr Tubman’s running mate is former footballer George Weah, who was defeated by Mrs Sirleaf in the 2005 poll.
Former rebel leader Prince Johnson, who came third in the first round with 12%, has urged his supporters to back Mrs Sirleaf