The United States and former colonial power France voiced alarm over the unrest gripping the poor West African nation and appealed for calm.
Hundreds of people broke through a heavy security cordon and stormed the National Assembly building in the capital Ouagadougou, ransacking offices and setting fire to cars, before attacking the national television headquarters and moving on the presidential palace.
One man was killed in the chaos that erupted just before lawmakers were due to vote on the legislation that would allow Compaore -- who took power in a 1987 coup -- to contest next year's election, AFP correspondents said.
The government, facing its worst crisis since a wave of mutinies shook the country in 2011, later announced it was calling off the vote but it was not immediately clear if this was a temporary move.
Black smoke billowed out of smashed windows at the parliament building, where several offices were ravaged by flames, including the speaker's office, although the main chamber so far appeared to be unscathed.
Several hundred protesters also broke into the headquarters of the national television station RTB, pillaging equipment and smashing cars, the correspondents said.
Crowds of people later massed near the presidential palace but were being held back by troops from the presidential guard who fired warning shots into the air.
The ruling party headquarters in the second city of Bobo Dioulasso and the city hall was also torched by protesters, witnesses said.
"The president must deal with the consequences," said Benewende Sankara, one of the leaders of the opposition which had called for the people to march on parliament over the Compaore law.
The country has been tense for days over the constitutional changes.
Police were out in force around the parliament after mass rallies earlier this week but failed to stop the onslaught despite using tear gas against the protesters.
The United States said it was "deeply concerned" about the crisis and criticised the attempts to alter the constitution, while France appealed for calm and said it "deplored" the violence.
The European Union had also urged the government to scrap the legislation, warning it could "jeopardise... stability, equitable development and democratic progress".
Several thousand protesters had marched through the capital on Wednesday, the day after street battles erupted during a mass rally by hundreds of thousands against what they branded a constitutional coup by supporters of the 63-year-old strongman.
The legislature had been due to examine a proposed amendment that would allow Compaore to run for re-election in November 2015.
"October 30 is Burkina Faso's Black Spring, like the Arab Spring," said Emile Pargui Pare, an official from the opposition Movement of People for Progress (MPP).
Government spokesman Alain Edouard Traore issued a statement Wednesday hailing the "vitality" of Burkina Faso's democracy despite what he termed anti-government "misbehaviour".
Compaore's bid to cling to power has angered many, including young people in a country where 60 percent of the population of almost 17 million is under 25.
Many have spent their entire lives under the leadership of one man and -- with the poor former French colony stagnating at 183rd out of 186 countries on the UN human development index -- many have had enough.
The situation is being closely watched across Africa where at least four heads of state are preparing or considering similar changes to stay in power, from Burundi to Benin and the Democratic Republic of Congo.
Compaore was only 36 when he seized power in the coup in which his former friend and one of Africa's most loved leaders, Thomas Sankara, was ousted and assassinated.
He has remained in power since, re-elected president four times since 1991 -- to two seven-year and two five-year terms.
In 2005, constitutional limits were introduced and Compaore is coming to the end of his second five-year term.
The opposition feared the planned new rules would enable Compaore to seek re-election not just once, but three more times, paving the way for up to 15 more years in power.
The third largest party in parliament had said it would back the amendment, which would have given the ruling party the two-thirds majority needed to make the change without resorting to a referendum.
Known in colonial times as Upper Volta, the landlocked country became independent from France in 1960 and its name was changed to Burkina Faso ("the land of upright men") in 1984.
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