On Sunday, Turkish President Recep Tayyip Erdogan told crowds of supporters gathered outside his residence in Istanbul that parliament must consider the public demand for the death penalty to be applied in the case of the coup plotters.
"The issue of return of the death penalty is now raised. If the ruling party is ready, we will stay together and do everything necessary with peace of mind," Bahceli said at his party's weekly parliamentary group meeting at the Grand National Assembly of Turkey.
Death penalty was abolished in Turkey in 2004 to bring its legislation in line with the EU standards.
On Monday, at a joint news conference, EU foreign policy chief Federica Mogherini and US Secretary of State John Kerry called on Turkey to respect democracy and human rights in its response to the failed coup. Western politicians said that the introduction of the capital punishment would close the way for Turkey to enter the European Union.