Tensions between the two North Atlantic Treaty Organisation allies have been strained amid Turkey's detention of American pastor Andrew Brunson.
On Friday, Turkey's Foreign Ministry said Turkey would retaliate against the raising of steel and aluminum tariffs by the US administration.
Tariffs were also increased on cosmetics, rice and coal.
The Turkish lira hit an all-time low of 7.24 to the dollar on Monday, Aug. 13, driven down by concerns over Erdogan's calls for the central bank to loosen monetary policy, and by deteriorating ties with the United States.
Speaking in the Black Sea region of Turkey, Erdogan says there isn't any logical explanation for the recent fluctuations in the value of the Turkish lira, which closed the week trading at record lows against the dollar.
US Vice President Mike Pence also renewed his threats to Turkey on Wednesday, warning that he and Trump would "stand firm" until Brunson is released.
Global investors have been anxious by Turkey's high levels of foreign debt and Erdogan's refusal to allow the central bank to raise interest rates to support the currency, as experts say it should.
The emir "will discuss with the Turkish president bilateral relations and means of strengthening the existing strategic cooperation between the two countries in various fields", said a Qatar News Agency statement.
Brunson's lawyer, İsmail Cem Halavurt, filed the demand on August 14 around a week after his previous appeal was rejected by the Turkish court in the western province of İzmir.
The U.S. wants American evangelical pastor Andrew Brunson freed and cleared of terrorism-related charges he has faced since 2016, when Turkish authorities arrested him for allegedly aiding a failed coup attempt earlier that year.