Returns from the capital Sukhum and the northwestern Gagra region indicated Khajimba was fewer than 200 votes ahead of his main rival, Sergei Bagapsh. Trailing in third was former Foreign Minister Sergei Shamba, followed by former Prime Minister Anri Jergenia and Popular Party leader Yabub Lakoba.
Though only partial, the results are unlikely to end the controversy sparked by the 3 October election, a poll that the Organization for Security and Cooperation in Europe says lacked legitimacy.
Early on 4 October, Russian and Georgian media quoted an alleged official Abkhaz information website as saying Khajimba had garnered 53 percent of the votes -- enough to be elected in the first round.
But the Central Election Commission subsequently denied these claims, saying not all polling stations had filed their returns and that no official results were yet available.
Addressing reporters in Sukhum this morning, Central Election Commission chief Sergei Smyr said his office had yet to receive voting protocols from the southern Gali region.
"As of today, Gali region's election commissions number 33, 34, and 35 have still not filed their protocols," Smyr said. "So, please, do not rush to conclusions. We still have time and we will do our utmost to speed up the [vote counting] process."
The Gali region is largely populated by ethnic Georgians who recently returned after being driven from their homes during the 1992-93 separatist conflict that led to Abkhazia's de facto independence. Bagapsh, who is married to a Georgian, is said to enjoy much greater popularity in Gali than Khajimba.
The Khajimba camp says most of the alleged fraud occurred in Gali. It has hinted that it may demand that results there be nullified.
In comments to reporters on 4 October, Khajimba's campaign chief Guram Inapshba accused Bagapsh's supporters of cutting off power to Gali polling stations after the vote in a bid to prevent pro-government observers from monitoring the counting of ballots.
Khajimba himself claimed that many Gali residents were forced through intimidation to cast their ballots for his main rival.
Bagapsh denies the accusations. On 4 October, the head of the Chernomorenergo power company claimed victory as dozens of his supporters picketed the Central Election Commission building to demand that results be published as quickly as possible:
"We won these elections. We garnered slightly over 51 percent of the votes -- 51.3 or 51.4 percent," Bagapsh said. "In absolute numbers, that amounts to more than 45,000 votes. The rival campaign staff got 28,000 votes. The difference between [us] is somewhere around 17,000 votes."
Abkhazia has only 120,000 registered voters, of which 80,000 took part in the polls.
A nongovernmental organization known as the Voters' League for Fair Elections, on 4 October rejected Khajimba's claims of election fraud. Group member Nadezhda Venediktova told RFE/RL's Georgian Service that Bagapsh was likely the winner.
"The Voters' League for Fair Elections and its offices were able to organize a parallel count," Venediktova said. "The Central Election Commission has not yet published the results of the vote and I don't think they will do it until [today]. [Bagapsh] say he garnered 51.1 percent of the votes and that Khajimba won only about 32 percent. I believe this roughly reflects the reality."
Although Bagapsh is backed by Amtsakhara -- an influential nationalist grouping whose core is made up of veterans of the war with Georgia -- political analysts in Tbilisi generally consider him a more suitable interlocutor than Khajimba.
They argue that the Georgian government may find it easier to negotiate a compromise on the status of the Black Sea region with a genuine nationalist rather than with someone who is widely seen in Tbilisi as Russia's man.
Georgia's minister for conflict resolution, Giorgi Khaindrava, on 4 October said he suspected Moscow would do its utmost to secure Khajimba's victory.
"We suspected from the very beginning that Khajimba would be appointed. Khajimba has no chance of winning an election because he is not a political figure. He never was a political figure. He is just an agent of [Russia's] FSB [Federal Security Service]," Khaindrava said. "Before that he was an officer of [Soviet] Georgia's [State] Security [Committee, or KGB]. His being appointed will put him in a position to lobby the interests of his parent administration."
Khajimba's official biography says he ran Abkhazia's National Security Ministry from 1989 through 2001. He then took over as deputy prime minister and defense minister, before finally becoming prime minister of the separatist government. During the 1992-93 war, he was in charge of the separatist forces' intelligence and counterintelligence in one of the conflict zones.
Russia has made little secret that it would prefer political continuity in Abkhazia and publicly endorsed President Vladislav Ardzinba's heir apparent.
Russian President Vladimir Putin in August met with Khajimba is the Black Sea resort of Dagomys -- a move that stirred protests from Georgia.
On 4 October, the Russian Foreign Ministry issued a brief statement describing the Abkhaz polls as "democratic" and expressing hope that peace talks between Georgia and its separatist region would soon resume.
But the chairman in office of the Organization for Security and Cooperation in Europe (OSCE) described the election as "illegitimate and unacceptable."
Reiterating his support for Georgia's territorial integrity, Bulgarian Foreign Minister Solomon Pasi also said no election can be held in Abkhazia until all refugees and internally displaced persons are able to return home "in safety and dignity."