They also held a meeting with President Masoud Barzani to discuss their agenda.
The United States has asked Iraq's Kurds to postpone a referendum on the independence of their autonomous Kurdish region, planned for September 25, the Kurdish presidency said.
The United States and other western nations are anxious that the vote could ignite a fresh conflict with Baghdad and turn into another regional flashpoint.
The referendum would in any case be non-binding and is strongly opposed by neighbours Iran and Turkey, which have sizeable Kurdish minorities of their own.
The date of the referendum stands as it is, September 25, Dakhil said. Iran has also said that such a referendum would not be appropriate.
US Secretary of State Rex Tillerson asked Barzani to postpone the referendum during a phone call on Thursday, Zebari told Reuters.
Barzani told Tillerson that the kind of coexistence that the Kurdistan Region had worked for with Iraq in the past and over various stages was not implemented, and that is why Kurdistan chose to take its own path, the statement continued. The Kurdish president declined, saying the U.S. administration has failed to provide guarantees or an "alternative" that would secure the future of Kurdistan.
Washington has urged Iraqi Kurdish leader Massud Barzani to postpone an independence referendum scheduled for next month but he requested something in return, his office said yesterday.
Tillerson said the KRG's decision to send a delegation to Baghdad was to find solutions to political issues through dialogue, the statement said.
The US state department said in June that it was concerned that the referendum would distract from "more urgent priorities" such as the defeat of ISIL.
The militants remain however in control of territory in western Iraq and eastern Syria.
Barzani's father led struggles against Baghdad in the 1960s and 1970s.
The ethnically-diverse city of Kirkuk remains the subject of dispute between northern Iraq's semi-autonomous Kurdish Regional Government (KRG) and Iraq's central government in Baghdad.
Responding to the Kurdistan leadership's move, Iraqi government spokesman Saad Hadithi said that Baghdad would not back any unilateral steps taken by Iraqi Kurdistan aimed at gaining independence, as such moves would violate the country's constitution.
Iran-backed Iraqi Shi'ite militias threatened to expel the Kurds by force from this region and three other disputed areas: Sinjar, Makhmour and Khanaqin.