Footage showed people throwing papers from the building’s windows, while others were seen entering the office of President Sooronbai Jeenbekov, BBC reported.
The break-in follows a day of clashes with police, who initially dispersed crowds with water cannon and tear gas.
The clashes come amid allegations of vote-rigging in last Sunday’s election.
Following the vote, only four parties out of 16 passed the 7% threshold for entry into parliament, three of which have close ties to President Jeenbekov.
On Monday, police used stun grenades to disperse thousands of protesters in Ala-Too square, before following them into nearby streets.
But demonstrators later flooded back into the central square.
About 120 people have reportedly been injured, half of whom were law enforcement.
Several people are in serious condition, but there have been no deaths, the health ministry said in a statement.
Protesters also released Kyrgyzstan’s former President Almazbek Atambayev, who was being held in a remand centre at the State National Security Service awaiting a trial for corruption offences, the local AKIpress news agency reported.
Groups close to the president have been accused of vote-buying and voter intimidation – claims international monitors say are “credible” and a cause for “serious concern”.
On Monday, 12 opposition parties jointly declared that they would not recognise the results of the vote.
Later, President Jeenbekov’s office said that he would on Tuesday meet leaders from all 16 parties that competed in the election, in a bid to defuse tensions.
One candidate, Ryskeldi Mombekov, told a crowd of more than 5,000 protesters on Monday: “The president promised to oversee honest elections. He didn’t keep his word.”
Mr Mombekov’s party, Ata Meken, had been confident of entering parliament, but in the end it was one of the eight parties that missed the threshold. Ata Meken leader Janar Akaev suffered a leg injury in the protests on Monday.
Protesters were also calling on President Jeenbekov to resign.
Thomas Boserup, head of the election observation mission of the Organisation for Security and Cooperation in Europe (OSCE), said in a briefing that although the vote had been “generally well organised”, allegations of vote buying were a “serious concern”.
President Jeenbekov’s younger brother, Asylbek Jeenbekov, is a member of Birimdik.
Mekenim Kyrgyzstan, meanwhile, is seen as being closely connected to the powerful Matraimov family. The family’s figurehead, Rayimbek Matraimov, was the target of anti-corruption protests last year and is believed to have helped finance Mr Jeenbekov’s successful presidential campaign in 2017.
Late on Monday, Birimdik announced that it would be open to a re-run of Sunday’s election, and called on other parties that had crossed the 7% threshold to do the same.