Tens of thousands of demonstrators came out on the streets of Turkey's capital Ankara and other cities to show support for the President, Recep Tayyip Erdogan.
On Sunday he told crowds of supporters, called to the streets by the government and by mosques across the country, that parliament must consider their demands to apply the death penalty for the plotters.
"We cannot ignore this demand," he told a chanting crowd outside his house in Istanbul late on Sunday. "In democracies, whatever the people say has to happen."
He called on Turks to stay on the streets throughout the week, and late into Sunday night his supporters thronged squares and streets, honking horns and waving flags.
Turkey gave up the death penalty in 2004 as part of a programme of reforms required to become a candidate to join the EU. Germany said on Monday that Turkey would lose its EU status if it reinstated the death penalty.
Yildirim said Turkey should not act hastily over the death penalty but could not ignore the demands of its people.