When Rwasa initially disappeared his party said that he had gone away on holiday. He is thought to be in the neighbouring Democratic Republic of Congo.
The Forces for the National Liberation (FNL), a former rebel group, was the ruling party's main competition until it pulled out of this weeks election, leaving Pierre Nkurunziza, the incumbent president, as the only presidential candidate.
The presidential election was held against the backdrop of daily grenade blasts that threatened to push the country back into civil strife, with at least ten people killed and more than 60 wounded.
|A spate of grenade attacks marred the elections and killed at least 10 people
The FNL has been accused of carrying out the grenade attacks, and police last week searched Rwasa's home.
"I got a lot of threats telling me if I do not accept the victory of the ruling party ... I will be arrested like former DRC deputy president Jean Pierre Bemba," Rwasa said in his statement.
"The government plans to jail me, pretending to have proof that I have distributed weapons with the aim of destabilising security in the capital Bujumbura. All this is nonsense."
Burundi's attorney general has said that there is no warrant for Rwasa's arrest.
The country has enjoyed relative peace since the FNL, the last group of Hutu fighters operating in the country since the Burundi civil war, agreed last year to lay down weapons and join the government.
Results of Monday's presidential vote are due to be released later on Wednesday.