Cavusoglu said the ministers had discussed steps both countries could take to solve the existing problems.
Also Turkish Foreign Minister said he told US Secretary of State Mike Pompeo that threats and sanctions will not work, after Washington targeted Turkish ministers over the detention of an American pastor. "However, Turkey always wishes to resolve these issues via diplomacy, dialogue and mutual understanding", Cavusoglu told reporters after meeting his US counterpart Mike Pompeo in Singapore.
Cavusoglu called his meeting with Pompeo "constructive".
The meeting came on the sidelines of the Association of Southeast Asian Nations (ASEAN) foreign ministers' meeting.
Turkish Foreign Minister Mevlut Cavusoglu on Friday said he told his USA counterpart Secretary of State Mike Pompeo that threats and sanctions would not work after Washington targeted Turkish ministers over the detention of an American pastor.
"The Turks were on notice that the clock had run out and it was time for Pastor Brunson to be returned and I hope they'll see this for what it is: a demonstration that we're very serious", he told reporters. "Pretty straightforward. They've been holding these folks for a long time". Turkey has said the sanctions are unacceptable.
The Erdogan government has vowed to retaliate against the US sanctions, announced Wednesday, but has not revealed what they will be.
Foreign Minister Mevlut Cavusoglu, who is set to meet US Secretary of State Mike Pompeo in the next few days, also warned that the move "will not go without response".
On Friday, the two leaders agreed to work together to resolve tensions between the two countries.
Pastor Andrew Brunson was held in prison for almost two years before he was moved to house arrest last week, disappointing American officials who expected his release.
"I am hopeful that we can".
The sanctions freeze any property or assets on United States soil held by the two ministers, and bar USA citizens from doing business with them.
Brunson, 50, was arrested in 2016 on charges of "committing crimes on behalf of terror groups without being a member" and espionage. The sanctions also prevent American citizens from doing any business with the two ministers. Although he was released to home detention, he faces a prison sentence of up to 35 years if he is convicted on both counts at the end of his ongoing trial. Gulen denies the claim.