The self-styled president of the region, Aslan Bzhania, said he had no intention of stepping down or fleeing. He said talks were proceeding with opposition representatives.
But opposition representatives rejected the president's statement and news reports said they had broken off the talks.
Russia said it was following the "crisis situation" with concern and urged its citizens to avoid travel to Abkhazia.
Russians tourists have long flocked to the self-proclaimed Republic of Abkhazia on the Black Sea. (EPA PHOTO)
Russia recognised Abkhazia and another breakaway region, South Ossetia, as independent states in 2008 after it defeated Georgia in a five-day war. It maintains troop bases in both regions and props up their economies.
In Abkhazia's capital Sukhumi on Friday, protesters used a truck to smash through the metal gates surrounding parliament. They then climbed through windows after wrenching off metal bars.
An opposition leader, Temur Gulia, said protesters initially demanded to scrap the investment agreement, which critics feared would allow wealthy Russians and businesses to buy up property in the lush Black Sea region, pricing out locals.
But now, he said, the protesters wanted to oust the president.
Protesters also broke into presidential administration offices located in the same complex as the parliament. Emergency services said at least nine people were taken to hospital.
Bzhania, writing on the Telegram messaging app, said he and other leaders were "staying in place and will keep on working".
"I ask you not to give in to panic. I am staying in Abkhazia and will work as I have done," Bzhania wrote, saying that the first task was to clean up after the unrest.
"At this time, talks are going on with the opposition."
Opposition activist Akhra Bzhania rejected the statement, telling Reuters the president had "lost his legitimacy. His refusal to resign today does not change anything."
Abkhazia's President Aslan Bzhania has held an emergency security council meeting over the protests. (AP PHOTO)
TASS news agency quoted opposition representative Kan Kvarchia as saying all talks had been broken off.
President Bzhania's office later said the president, a former chief of the state security service who became head of state in 2020, was in his coastal home village of Tamysh.
Another opposition leader, Eshsou Kakalia, told Reuters the protesters would not leave the government complex until Bzhania agreed to resign.
The presidential administration said in a statement that authorities were preparing to withdraw the investment agreement.
If Bzhania fell, he would be the third local leader to be toppled in a similar way since 2008. Vartanyan said Moscow's usual approach was to allow the periodic crises to play out, and then strike deals with whichever leader came next.
Most of the world recognises Abkhazia as part of Georgia, from which it broke away during wars in the early 1990s.
The opposition said in a statement that the protests were not against Russian-Abkhazian relations, but charged that President Bzhania "has been trying to use these relations for his own selfish interests, manipulating them for the sake of strengthening his regime".
