"Secretary Blinken made clear that the United States will not normalize relations with (Syria) and does not support others normalizing until there is authentic, UN-facilitated political progress in line with UN Security Council Resolution (UNSCR) 2254," the State Department said, according to Al Jazeera.

The Arab League suspended Syria’s membership in 2011, when the Arab country found itself in the grip of overwhelming foreign-backed militancy and terrorism.

Back then, the body cited, what it called, Syria's alleged crackdown on opposition protests as the reason behind its decision. Syria has denounced the move as lacking in legal foundation and "a violation of the organization’s charter."

With support from Iran and Russia, the Syrian government has regained control of much of the country and some Arab countries have begun to soften their stance towards Damascus. But the US has maintained its opposition to President Bashar al-Assad without an inclusive political settlement to the conflict.

Blinken expressed gratitude to Jordan for hosting refugees.

The remarks came as several regional Arab states -- including Saudi Arabia, the United Arab Emirates, and Egypt -- have been trying to reengage with Syria, sending over their senior officials at the head of ranking delegations for talks with Assad.

Speaking earlier, Secretary General of the Arab League Ahmed Aboul Gheit said a series of meetings would be held initially to assess the process of restoration of Damascus' role within the body.

Assad would be invited to an upcoming Arab League summit in the Saudi capital of Riyadh once member states reach a consensus on the matter, he noted.