The open letter was posted on May 30 on the opposition online website Charter-97.
In his statement, Sannikau says he does not recognize the official result of the presidential election held on December 19 that declared incumbent President Alyaksandr Lukashenka the winner.
International election monitors said the vote was flawed.
"The worst predictions about the possible development of the situation in Belarus after the presidential election turned out to be true," Sannikau wrote. "The incompetence of the country's current leadership to run the country has been proven long ago, but now it is becoming more and more obvious, as the economic situation in Belarus is in grave condition."
Sannikau reiterated his view that the December 19 presidential elections were illegitimate and rigged.
"It was clear that the first round of the election did not produce a winner, and therefore a second round of voting should be held," he said. "President Lukashenka should accept that he failed to get at least 50 percent of votes, and since the [Central Election Commission] rated me second after Lukashenka in terms of the number of votes, I am ready to take part in the second round of the elections that should be held under international control."
Sannikau was arrested after some 15,000 people took part in antigovernment demonstrations on December 19 to protest the announcement of Lukashenka's reelection. He was found guilty of organizing mass riots and sentenced on May 14 to five years in prison.
Hundreds of protesters were arrested at the demonstration and in the succeeding days, including almost all opposition presidential candidates.
Read more in Belarusian here