Censor.NET reports citing Reuters.
Turkey abolished capital punishment in 2004, allowing it to open EU accession talks the following year, but the negotiations have made scant progress since then.
With pro-government protesters demanding that the coup leaders be executed, Erdogan said on Sunday there could be no delay in using capital punishment and the government would discuss it with opposition parties.
Merkel told Erdogan on the phone that the European Union and Germany vehemently oppose the reinstatement of the death penalty and that such a step is "in no way compatible" with Ankara's goal of EU membership.
Merkel's spokesman Steffen Seibert told a news conference earlier on Monday that Germany and the EU categorically reject the death penalty.