However, he left the door open for the sentence to be reintroduced through parliamentary consensus.
Speaking to reporters at Cankaya Palace in the capital Ankara, he said those convicted of involvement in Friday’s failed military coup would face the most severe punishment under the current legal system.
Turkey outlawed the death penalty in 2004 but there have been growing calls for its return following the coup attempt, which saw more than 240 people lose their lives.
“Democracies cannot disregard the demands of the public,” Kurtulmus said. “Currently, capital punishment is not on the agenda of our government. However, if the public demands and the negotiations with other parties in parliament really require something like this, it belongs among the next steps.”
The government has said the attempted coup was organized by the followers of U.S.-based Fetullah Gulen, who is accused of a long-running campaign to overthrow the state.
U.S. extraditing Pennsylvania-based preacher, Fetullah Gulen, to Turkey over his alleged involvement in Friday’s deadly coup attempt would be the "greatest sign of solidarity", Kurtulmus said.
Kurtulmus responded that "sending Fetullah Gulen to Turkey would be the number one solidarity display".
There are currently 9,322 suspects linked to the failed coup attempt on late Friday and all of them are going through legal procedures, Kurtulmus said.
Kurtulmus said there is "no proof" that any country, including the U.S., was involved in Friday’s failed coup attempt, which occurred late on July 15 when rogue elements of the Turkish military tried to overthrow the country's democratically elected government.
At least 208 people, including members of the security forces and civilians, were martyred in Istanbul and Ankara and nearly 1,500 others wounded as they protested against the coup.
The government has said the attempted coup was organized by followers of U.S.-based preacher Fetullah Gulen, who is accused of a long-running campaign to overthrow the state through supporters within Turkish institutions, particularly the military, police and judiciary, forming the so-called parallel state.