Jose Fortunati admitted the Estadio Beira-Rio is not yet ready to host matches for this summer's tournament in an interview with a local radio station.
The inside of the stadium is almost complete, but there are serious problems with the outside of the ground.
Organisers still need to build temporary structures for the media, sponsors and other groups, in line with FIFA requirements - and they are not allowed to use public money to do it.
Fortunati has demanded a bill that will exempt companies investing in temporary structures needed at the stadium from paying tax, saying it is the only way for the city to raise the necessary needed funding.
"This is the point which matters in terms of holding the World Cup in Porto Alegre," he told Radio Gaucha. "If the bill is not voted, we will not have the World Cup in Porto Alegre.
"This is because we will not have the resources to do it. We have no plan B. The only alternative is this."
Porto Alegre, located in the south of Brazil, is scheduled to play host to four group matches and a last-16 clash.
The first match is France v Honduras on June 15. The second is Australia v Netherlands on June 18. The third is South Korea v Algeria on June 22, before Nigeria face Argentina on June 25.
The final match is the last 16 match between the Group G winner and Group H runner-up.