"The killing sprees we saw in countries like Iran and Iraq were shameful," Salil Shetty, Amnesty International's Secretary General, said in a statement.
"Only a small number of countries carried out the vast majority of these senseless state-sponsored killings."
It listed the known methods of execution, including beheading in Saudi Arabia, electrocution in the US and lethal injection in China, Vietnam and the United States. Several countries were listed as using hanging and shooting.
Europe, however, remained execution free in 2013 for the first time since 2009, although Belarus - the only country to still enforce the death penalty - sentenced four people to death.
At least 23,000 people were on death row across the world as of the end of 2013. It also counted 1,925 people sentenced to death in 57 countries last year, up from the year before.
"We oppose the death penalty in all cases, without exception," Jose Luis Diaz, the group's representative at the United Nations, said on Wednesday. "It is the ultimate cruel, inhuman and degrading punishment."
The 10 places where most executions were carried out in 2013:
1. China
Amnesty International does not have an official figure on executions in China during 2013, but believes the figure to be in the thousands.
2. Iran
Iran carried out 369 public executions.
3. Iraq
Iraq committed 169 public executions in 2013.
4. Saudi Arabia
Saudi Arabia carried out 79 executions in 2013.
5. USA
Thirty-nine people were executed in the US in 2013.
6. Somalia
In Somalia, 34 people were publicly executed last year.
7. Sudan
Twenty-one people were executed in Sudan.
8. Yemen
Thirteen people were executed in Yemen in 2013.
9. Japan
Eight people were executed in Japan, according to the report.
10. Vietnam
Vietnam does not release public figures on executions but Amnesty estimate the number to be a minimum of seven.
- THE INDEPENDENT