Mr Tubman was speaking a day after Liberia’s opposition parties – including that of Mr Tubman – said first-round counting was fraudulent.
Partial first-round results give President Ellen Johnson Sirleaf a slight lead over Mr Tubman.
Mrs Sirleaf’s party had said she will take part in a run-off, even unopposed.
The chairman of the Liberian National Election Commission (NEC), James Fromayan, has rejected any accusations of electoral fraud.
Mr Tubman told the BBC’s Newshour programme: “We will participate in the run-off because we believe that the figures as they have emerged do not allow for anyone to win the first round.
“Therefore the focus must be on the second round and so we are beginning to rally our people.”
Earlier, Liberian opposition parties called on their supporters to join a rally on Sunday in protest against the presidential election, although it was not clear where or when it might take place.
Latest results published by the election commission, with 80% of the votes counted, put Mrs Sirleaf on 44.6% of the vote, while Mr Tubman polled 31.4% and former warlord Prince Johnson had 11.2%.
On Saturday, opposition parties – including those of Mr Tubman and Mr Johnson – said they could offer photographs and witnesses to back their claims that the NEC had manipulated vote-counting in favour of President Sirleaf.
Mr Fromayan said any grievances should be channelled through the complaints process.
Mrs Sirleaf’s Unity Party said it was not surprised by the allegations.
“They are doing this thing because it is not going their way,” said party secretary-general Wilmot Paye.
This is the first election organised by Liberia’s NEC – the previous one was run by the UN.
President Sirleaf, who was first elected in 2005 and is viewed abroad as a reformer, was awarded the Nobel Peace Prize last week for her role in stabilising the West African nation after a 14-year civil war.
Mr Tubman is running under the banner of the Congress for Democratic Change (CDC) party, with former football star George Weah as his running mate.
Mr Weah was beaten by Mrs Sirleaf in the 2005 poll.
Prince Johnson has said he is looking forward to playing the role of kingmaker, AP news agency reported.
His forces infamously filmed the torture and murder of dictator Samuel Doe in 1990.
After the war, he became a born-again Christian pastor and was elected to the senate in the 2005 poll.