Azerbaijani journalists and human rights activists have appealed to Fatullayev to "conserve his health for the fight against dictatorship."
Fatullayev's father, Emin Fatullayev, visited him on October 26. Emin Fatullayev told RFE/RL his son did not intend to end the protest.
He also said Eynulla "has no health problems, doctors measure his blood pressure and monitor his condition."
Fatullayev, editor of the independent newspaper "Realny Azerbaijan," was sentenced in 2007 to 11 years in prison on charges including tax evasion and fomenting interethnic hatred.
Rights organizations believe the charges against him were fabricated.
Fatullayev began the hunger strike to demand the Azerbaijani authorities comply with an April 22 ruling by the European Court of Human Rights (ECHR) in Strasbourg that he be released immediately and paid 25,000 euros ($34,467) in compensation.
An Azerbaijani Supreme Court spokesman told local media this week the court might convene an ad hoc session to discuss the ECHR ruling.
Fatullayev was sentenced in July to an additional 2 1/2 years in prison after a trace amount of drugs were allegedly found in his prison cell. Fatullayev said the drugs were planted.