The United States and Turkey support differing rebel groups fighting the Syrian government, while Russian Federation and Iran back Assad's government in the war.
"We brought forward proposals on how we can address all of the critical issues that are standing between our countries", Tillerson said during a joint news conference with Cavusoglu.
Turkey on Saturday denied allegations that it had used poisonous gas during operations in the northwestern Afrin region of Syria, following accusations from a human rights group and local news outlets. Tillerson said the United States would look at any evidence Turkey presents, which in the past has been judged by courts to be insufficient for the extradition Turkey wants.
The incursion has created an unprecedented military face-off between the two largest armies in North Atlantic Treaty Organisation, with USA forces fighting alongside the YPG in northeastern Syria while Turkey attacks members of the group to the west.
An attempt by Syrian government forces to protect the country's northern borders could see them come into direct conflict with the Turkish troops who are engaged in a cross-border offensive against the YPG in Afrin.
The United States has armed, trained and aided YPG fighters with air support and special forces, as the main ground force in its campaign against the Islamic State of Iraq and the Levant militant group.
UML names KP Sharma Oli as Nepal's next Prime Minister
Oli blamed the blockade on Delhi and tilted Nepal's diplomatic relations towards China , stoking nationalistic sentiment. Nepali democracy has struggled to achieve stability since parliamentary representation was introduced in 1990.
Syrian Kurdish forces and a monitoring group said the Turkish military carried out a suspected gas attack that wounded six people in Syria's Afrin region on Friday. "We were either going to correct this or it was going to take a turn for the worse".
Those talks followed a lengthy meeting of Turkish President Recep Tayyip Erdogan, Cavusoglu and Tillerson late Thursday at which a broad range of disagreements were covered.
Turkish officials say the Kurdish militias in Afrin have fired more than 100 rockets and mortars over the border into Turkey in that time, killing seven civilians and one soldier in a border observation post. The Turkish view of the connection between the two groups was bolstered this week by a USA intelligence assessment equating them and concluding they "probably will seek some form of autonomy" - exactly what Turkey fears.
Hedu further noted that Turkish troops actually did not advance in Afrin, but engaged in hit-and-run tactics instead.
Turkey has said it could expand its assault to those areas and last week renewed its demands for the YPG to pull out of all parts of Syria west of the Euphrates.