Internacional were also angry after they were left facing four games in eight days as the Brazilian Football Confederation (CBF) re-scheduled fixtures which had been postponed so that some clubs, including Sao Paulo and Santos, could play friendly matches in Europe.
"The law is that there has to be 66 hours between matches and we are only going to play if this is respected," Nautico president Paulo Wanderley told reporters.
"Nautico have nothing to do with Sao Paulo's excursion or the friendly that Santos played against Barcelona," added Wanderley, whose club are due to play Sao Paulo at home on Sept. 3 and Vasco da Gama two days later.
Internacional were left with an even more daunting task, facing Corinthians (September 4), Ponte Preta (September 7), Santos (September 9) and then Vitoria (September 11).
"Clearly, this has adversely affected Inter," the club's football director Marcelo de Medeiros told Radio Gaucha.
"We don't agree at all with this, which is happening because another club went on an excursion abroad. We are being forced to play on a Saturday and then a Monday, which is against the rules of the competition."
The CBF said it was forced to make the changes as it had run out of free dates.
Brazil is unique among major football nations in holding regional competitions, which take up the first four months of the season.
As a result, the 20-team Brazilian championship, in which each team has to play 38 matches, is squeezed into just over six months between mid-May and the start of December.
This season was further complicated by a two-week break as the country hosted the Confederations Cup.