The country's constitution has prohibited re-election since it was passed in 1992 after a brutal dictatorship fell in 1989.
"A coup has been carried out. We will resist and we invite the people to resist with us," said Senator Desiree Masi from the opposition Progressive Democratic Party.
Firefighters managed to control the flames after protesters left the Congress building late on Friday night. But protests and riots continued in other parts of Asuncion and elsewhere in the country well into the night, media reported.
Earlier, television images showed protesters breaking windows of the Congress and clashing with police, burning tires and removing parts of fences around the building. Police in riot gear fired tear gas and rubber bullets.
Several politicians and journalists were injured, media reported, and Interior Minister Tadeo Rojas said several police were hurt. One member of the lower house of Congress, who had been participating in protests that afternoon, underwent surgery after being hit by rubber bullets.