Kurdish People s Protection Units (YPG) fighters .(FILE AFP)
The government of President Bashar al-Assad rejects the Kurdish administration in north and northeast Syria and accuses it of "separatism".
Several rounds of talks since 2018 between Damascus and the Kurds -- who control most of the country's major oil and gas fields -- have failed to achieve any results.
"We affirm our readiness to meet and talk with the Syrian government and with all Syrian parties to hold discussions and present initiatives for a solution," the Kurdish authorities said.
The statement denied any separatist ambitions, "affirming Syria's territorial integrity" and calling for Syria's resources to be shared "fairly".
The Kurdish-led Syrian Democratic Forces (SDF), the Kurdish administration's de facto army, spearheaded the fight against the Islamic State group in Syria, driving it from its last stronghold in the country in 2019 with US backing.
Assad has been politically isolated in the region since Syria's war began in 2011, but a devastating February 6 earthquake that killed thousands in Turkey and Syria sparked Arab outreach.
A flurry of diplomatic activity has been underway in past weeks as Middle East rivals Saudi Arabia and the Syrian government's ally Iran patched up ties, shifting regional relations.
On Tuesday, Saudi Foreign Minister Prince Faisal bin Farhan met with Assad in Damascus, in the first visit by a Saudi official since the conflict began.
The pair discussed steps to achieve a political settlement for Syria's return to the Arab fold, according to the Saudi foreign ministry.
Last week, diplomats from nine Arab countries met in Saudi Arabia to discuss ending Syria's long spell in the diplomatic wilderness, and Syria's foreign minister visited Saudi Arabia for the first time in over a decade.
The Kurds in the statement urged "Arab countries, the United Nations and international forces... to play an active and positive role in searching for a common solution".
They said they were ready to share resources including oil and gas "through an agreement with the Syrian government" following "dialogue and negotiation".
Turkey has also made overtures towards Damascus in recent months, stoking further fears among Syria's Kurds.
Ankara considers the People's Protection Units (YPG) -- which dominate the SDF -- as an offshoot of the banned Kurdistan Workers' Party (PKK), designated as a terrorist group by Turkey and its Western allies.
"Any party or individual working for a foreign power is simply a traitor and a collaborator," Assad told broadcaster Russia Today in an interview last month, when asked about the YPG.