Erdogan did not host a a summit meeting in Istanbul to approve a Cabinet list presented by Yildirim, who replaces the outgoing prime minister, Ahmet Davutoglu.
The 60-year-old Yildirim was selected by Erdogan on Sunday to form a new government after Davutoglu resigned over differences with the president. Yildirim has vowed to follow Erdogan's path and make constitutional changes to change Turkey into a presidential system.
Analysts maintain that Erdogan is trying to make changes in the Constitution because he wants to concentrate all available power in his hands. The political change in Turkey comes at a time when the nation is facing serious security threats including increased attacks by Kurdish and Islamic State militants.
Meanwhile, German Chancellor Angela Merkel on Monday told Erdogan of her "deep concern" over the state of democracy in Turkey. She also expressed doubt that a plan to offer Turks visa-free travel to the EU would be implemented on time.
Merkel also took a potshot t a law that critics believe is aimed at evicting pro-Kurdish lawmakers from parliament and stressed to Erdogan that a democracy needed "an independent judiciary, an independent press and a strong parliament".
"Of course, the lifting of the immunity of one quarter of the deputies is a source of deep concern. I expressed this to the Turkish president and we discussed these questions very openly," she said, adding: "Not all my questions have been answered, we will have to watch developments closely." On Friday, a controversial bill was adopted by Turkish parliament that would lift immunity for dozens of MPs.