Protesters had occupied the parliament in protest at an investment agreement with Russia.
Russian news agency RIA reported that President Aslan Bzhania had said on Saturday he would resign and hold a snap election once protesters vacated the parliament in Abkhazia's capital Sukhumi, and proposed a vice-president as interim head of state.
"When they leave the building, I will write my resignation letter and in the new election we'll see how much support they get," RIA cited Bzhania as saying.
He said he planned to run in that election.
Abkhazia leader Aslan Bzhania says he will resign if protesters leave the region's parliament. (AP PHOTO)
Crowds that gathered in Sukhumi rejected the deal and opposition leaders said they would only accept Bzhania's unconditional resignation.
"None of us have come here for the sake of seats (in parliament)," former Abkhazian prime minister Valery Bganba told the crowd.
"We came here to save our people, our country."
At least 14 people were injured on Friday when opposition protesters clashed with police, Russian state news outlet RIA Novosti reported.
MPs had gathered at the region's parliament building to discuss ratifying measures allowing Russian citizens to buy property in the breakaway state.
However, the session was postponed as demonstrators broke down the gate to the building's grounds with a truck and streamed inside.
Some threw rocks at police, who responded with tear gas.
Protesters said in a statement on Saturday that the occupation was not against Abkhazia's close ties with Russia but accused Bzhania of "trying to use these relations for his own selfish interests (and) manipulating them for the sake of strengthening his regime".
Bzhania, quoted by Russian news agencies, later told a government meeting held in his native coastal village of Tamysh that order would be restored.
He said protesters only controlled the parliament and government buildings they had occupied.
"The situation will stabilise, everything will return to a legal framework," RIA news agency quoted him as saying.
"We have a president, we have laws. We have a homeland that we all must serve."
Abkhazia's interior ministry and security service issued statements saying they would obey orders from the president.
Russia said on Friday it was following the "crisis situation" with concern and urged Russian citizens to avoid travel to Abkhazia.
Russia recognised Abkhazia and another breakaway region, South Ossetia, as independent states in 2008 after defeating Georgia in a five-day war.
It maintains military bases in both regions and props up their economies.
Most of the world recognises Abkhazia as part of Georgia, from which it broke away during wars in the early 1990s.
with AP
