More countries reject death penalty, but more people were put to death last year - 5,628 - than in either of the previous two years. China alone accounted for 5,000 executions.
Rome-based Hands Off Cain said the increase was because more countries that have capital punishment on their books actually resorted to it in 2006.
In its annual report on the death penalty, the group said the gradual trend of abolishing capital punishment continued, with 51 countries retaining the death penalty, compared with 54 in 2005. But it said 27 countries had used the death penalty in 2006, up from 24 in 2005.
As a result, the number of executions increased, to at least 5,628 last year compared with 5,494 in 2005 and 5,530 in 2004.
Overall, 146 countries and territories have renounced the death penalty to some extent, either through outright abolition or a moratorium, Hands Off Cain said.
The report said China remained the top executioner, with at least 5,000 confirmed executions and unconfirmed reports that as many as 8,000 people are put to death annually. The report cited Chinese officials and academics as saying executions had decreased, however - in part because of a new amendment requiring the Supreme Court to confirm all death sentences and public hearings for appeals.
Iran came in second in the group's top execution rankings. Hands Off Cain said Tehran doubled the number of people it put to death in 2006, executing at least 215 people compared with 113 in 2005, though it said the real number may be even higher.
Pakistan also nearly doubled the number of executions in 2006, putting at least 82 people to death last year compared with 42 the year earlier.
Hands Off Cain said both Iran and Pakistan executed minors, in violation of the U.N. Convention on the Rights of the Child.
The United States remained the only country in the Americas that carried out a death sentence in 2006. Fifty-three people were executed in the United States in 2006, down from 60 in 2005 and 59 in 2004, the group said.
Hands Off Cain was honoring Rwandan President Paul Kagame with a special award Thursday for his role in ending the death penalty in his country. Earlier this year, the government approved a bill abolishing capital punishment, in part to encourage European and other countries to extradite suspected masterminds of the country's 1994 genocide.
Rwanda has also signed on as a co-sponsor to a U.N. General Assembly resolution calling for a worldwide moratorium on executions.
Rwanda's actions, the group said, were of "exceptionally symbolic value, through which Rwanda has emblematically shown the world the possibility of an end to the absurd cycle of vengeance and that justice and lawfulness cannot be achieved with capital punishment."
Hands Off Cain said it believed the U.N. resolution - which has failed in previous years - now has enough support to pass.
Italy has been at the forefront of the U.N. campaign.
Putin's Annual Address to the Federal Assembly is scheduled for September 30. Kremlin sources say it will become even more historic and globally important than his 2014 speech