By Agence France-Presse
Addressing inmates at the main Welikada prison, Sirisena promised financial support to re-integrate them in society, but made no reference to monk Galagodaatte Gnanasara, whose release was demanded Friday by the Buddhist hierarchy.
Sri Lanka has declared two days of holidays for nation-wide celebrations of Vesak, or the commemoration of the birth, enlightenment and passing away of the Buddha.
Those who benefited from the amnesty had been serving short jail terms for minor offences and none had been convicted of murder or rape, officials said.
The 762 released Saturday included several women.
"An increase in the prison population is a sign of the declining moral value of any country," Sirisena said in a nationally televised ceremony.
He said Sri Lanka's prison system was designed to accommodate 11,000 inmates but as of Saturday there were 24,332 convicts as well as remand prisoners in judicial custody.
Many Buddhist leaders had urged Sirisena to grant a special amnesty to monk Gnanasara on Vesak day.
Since December, Gnanasara has been serving concurrent jail sentences extending up to six years over his disruptive behaviour in court and intimidating a woman litigant.
He has long been accused of instigating hate crimes against minority Muslims in the Buddhist-majority country. The monk has denied involvement in anti-Muslim riots in 2014 that left four people dead.
His Bodu Bala Sena (BBS), or Buddhist Force, was not linked to the recent anti-Muslim riots that came after the April 21 suicide bombings blamed on Islamic extremists.
Gnanasara had maintained close ties with Wirathu, an extremist monk based in Myanmar, whose hate speech has stoked religious tensions in that country.
Wirathu visited Sri Lanka as a guest of Gnanasara shortly after the 2014 anti-Muslim riots at Sri Lanka coastal town of Aluthgama, and the duo vowed to fight what they called the threat to Buddhism from Islamic jihadists.