Tillerson to meet Qatari foreign minister in Washington
Tillerson's meeting with Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman al-Thani at the state department also comes days after Doha rejected a list of demands from Bahrain, Egypt, Saudi Arabia and the UAE.
The ultimatum demands that Qatar comply with 13 points in return for an end to a three-week-old diplomatic and trade blockade of the country.
Earlier this week, Tillerson said that the demands were being considered and called for a "lowering of rhetoric".
"While some of the elements will be very difficult for Qatar to meet, there are significant areas which provide a basis for ongoing dialogue leading to resolution," Tillerson said in a statement.
"A productive next step would be for each of the countries to sit together and continue this conversation."
The four Arab governments announced earlier this month they were suspending all ties with Qatar, accusing it of support for extremist groups - a claim Doha vehemently denies.
Meanwhile, Tillerson has urged a diplomatic solution, and Washington has been pushing for a clear list of grievances that are "reasonable and actionable".
Signalling Washington's mounting frustration at Riyadh's role in the crisis, state department spokeswoman Heather Nauert recently called on the parties to settle their differences.
She called into question whether Qatar's alleged support for terrorism is the true cause of the crisis or whether there is an underlying political dispute in what seems to be similar concerns voiced by Doha after the Gulf nations began announcing their intentions to cut diplomatic ties.
Qatar's neighbours closed their airspace to Qatari carriers and blocked its only land border, vital for food imports.
Qatar is home to the largest US base in the region, al-Udeid, and Bahrain is home to the US Navy's Fifth Fleet.