Bishkek - Jeenbekov said he feared that violence might break out if protesters carry out a threat to march on his compound.
"The military and security forces will be obliged to use their weapons to protect the state residence. Blood will be inevitably shed. I urge both sides not to fall for provocations," he said.
"I do not want to go down in Kyrgyzstan's history as a president who shed blood and shot at his own citizens."
After the election, opposition supporters took to the streets and seized government buildings, prompting the authorities to annul the vote. Jeenbekov announced last week that he would resign, but this week he delayed his exit, saying he would stay in office until a new election was held.
On Wednesday, Jeenbekov accepted parliament's choice of Sadyr Japarov, a nationalist whose supporters freed him from prison last week, to be prime minister. Japarov and his followers have demanded Jeenbekov leave office.
Kyrgyzstan, which borders on China, is a close ally of Russia and also hosts a large Canadian-owned gold mine.