BNP arranged the programme at the Jatiya Press Club marking the 45th death anniversary of great national leader Moulana Abdul Hamid Khan Bhasani.
Fakhrul said the physicians at Evercare hospital are saying it is not fully equipped to treat all the critical diseases of Khaleda. "So, her treatment at an advanced centre abroad is now very essential."
He said other political parties are also calling upon the government to allow the BNP chairperson to go abroad, but Awami League and its president Sheikh Hasina are not accepting it fully.
"We're again urging the government to take immediate arrangements to send Begum Khaleda Zia abroad for better treatment and saving her life. Don't bring politics with it," the BNP leader said.
He recalled Khaleda's contributions to the country's liberation war, restoration of democracy and its development.
"The contributions of our leader (to the country) are unmatched by any other living political leaders. Life and death are in the hands of Allah. We'll dedicate our lives, if necessary, to make every effort to save the life of our leader. Let's just get ready for it and work accordingly."
Khaleda, a 76-year-old former prime minister, was readmitted to Evercare Hospital on 13 November, six days after she had returned home from the hospital.
The BNP chief's physicians said she has been suffering from rheumatoid arthritis, diabetes, ophthalmological and dental complications.
They also said she is now suffering from a critical cardiac problem while her blood sugar is out of control and hemoglobin level in her blood has dropped.
On behalf of the family, Khaleda's younger brother, Shamim Iskander, submitted an application to the Home Ministry on 11 November urging the government to allow her to go abroad for better treatment.