Washington and Ankara are also at odds over the Syrian war, Turkey's plan to buy missile defenses from Russian Federation and the USA conviction of a Turkish state bank executive on Iran sanctions-busting charges this year.
Cavusoglu told Turkish press that the meeting was "constructive", but also spoke out against the sanctions.
Also caught in the spat is a plan for the United States military to deliver new F-35 fighter jets to Turkey.
Speaking to Turkish journalists after the meeting, Cavusoglu also described the discussion with Pompeo as "constructive", but added: "Nothing can be achieved through threatening language and sanctions".
Apple briefly becomes the first $1 trillion USA company
April 1976: Jobs, Wozniak and Ronald Wayne create Apple Computer to sell an eponymous computer hand-built by Wozniak. Five years ago, Apple was spending about US$4b a year on research and development, or about 3 per cent of its sales.
Erdogan said in a speech on Friday that his country was "face to face with an economic war", from which Ankara "will emerge victorious".
Erdogan said within the scope of action plan, the environmental impact assessment and survey project works of Canal Istanbul will be submitted for approval.
Brunson, 50, is being tried on espionage and terror-related charges, which he and the USA government vehemently deny.
On the sanctions, he said: "I hope they'll see this for what it is, a demonstration that we're very serious".
Pastor Brunson was arrested in Izmir, Turkey in October 2016, and was accused without any evidence of helping terrorist groups and of engaging in espionage.
NASA confirms delays in Boeing and SpaceX commercial crew flights
Four of the eight astronauts will nearly certainly be Bob Behnken, Eric Boe, Doug Hurley, and Sunita "Suni" Williams . However, both companies still have to prove that their vehicles can fly to the ISS and return safely to Earth.
Washington this week imposed sanctions on two Turkish ministers over the case of Andrew Brunson, a USA pastor on trial in Turkey accused of backing terrorism.
Turkish Finance Minister and President Recep Tayyip Erdogan's son-in-law, Berat Albayrak, said both sides wanted to continue dialogue.
The meeting was the first between the countries' officials after Ankara vowed it would respond to sanctions with retaliatory measures.
His language was immediately echoed by President Donald Trump, who had enjoyed a relatively warm relationship with Mr Erdogan and was even reported to have "fist-bumped" the Turkish president at a North Atlantic Treaty Organisation summit last month.
Gulen, who has lived in self-imposed exile in the USA since 1999, has denied any role in the 2016 coup attempt.
Bank of England hikes interest rates
In other words: when inflation is steady at the Bank's 2% target and the economy is running at its maximum speed limit. The six-member Monetary Policy Committee headed by RBI Governor Urjit Patel kept its stance at neutral.