Jihad al-Makdisi told reporters that he expected a deal to be signed soon.
He spoke after the expiry of the latest deadline set by the Arab League for Damascus to agree to its peace plan and allow observers to monitor it.
The head of the Arab League said he is studying the Syrian response, but noted that it contained new conditions.
Syria is under pressure to end its crackdown on an uprising the UN says has left more than 4,000 people dead, with reports of 17 new deaths on December 5 alone.
The Arab League had given the Syrian government until December 11 to sign its peace initiative and agree to the deployment of an observer mission, or face the imposition of further sanctions approved last week.
The new measures, officials said, would include freezing the assets of top officials and associates of President Bashar al-Assad, and banning them from other Arab countries. The number of flights to Syria would also be halved.
Some sanctions - including a ban on dealings with Syria's central bank, a halt to Arab government funding for projects in Syria, and a freeze of Syrian government assets - went into effect after Damascus failed to meet the last deadline to allow in observers on November 25.
The Syrian government complained that the Arab League's proposals would infringe on national sovereignty, although it did not reject them.
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