Fred Hoff made his remarks, in a bid to test Syria's support for Washington's efforts, after lengthy talks with Syrian Foreign Minister Walid Muallem in Damascus.
"Mr. Hoff underlined the United States' quest to work for achieving comprehensive peace in the region and its determination to play its effective and balanced role for resuming peace negotiations on all tracks," said an official statement.
Meanwhile, the Israelis said they were ready to resume direct talks with Damascus if it distances itself from Iran and armed Islamist groups in Lebanon and the Palestinian territories that are arrayed against the Jewish state.
The Israelis' assurances followed officials' meetings with Hoff during the adviser's four-day trip to Israel.
Syria dismissed the Israeli demand, insisting that any new negotiations should include assurances that it will recover the Golan Heights, which Israel captured in the 1967 war.
"Muallem underscored Syria's adherence to regaining the Golan Heights until the June 4th 1967 borderline in accordance with international legitimate resolutions," read the official statement carried by state-run Syrian Arab News Agency.
"The Minister highlighted Syria's keenness to achieve a just and comprehensive peace in the region according to the Madrid formula and land-for-peace principle," it said, adding both reviewed the "requirements" needed for the progress and success of the peace process. It gave no further details.
Hoff, who advises Mitchell on Syria and Lebanon, authored an academic proposal earlier this year for solving the Golan dispute by turning much of the strategic plateau into a nature reserve that would be accessible to both Israelis and Syrians.
Syrian President Basher Al-Assad has recently played down prospects for negotiations, saying he saw no partner in right-wing Israeli Prime Minister Benjamin Netanyahu, who took power in March.
It was not yet clear if Assad will be meeting with Hoff later in the day.
Turkey brokered four rounds of indirect talks between the two foes last year, the first such contacts since previous peace negotiations were broken off in 2000 over the fate of the Israeli-occupied land in the Golan Heights, along Syria's border.
But Syria froze contacts when Israel launched a devastating offensive against the Gaza Strip, controlled since June 2007 by the Islamic militant movement Hamas. Hamas' exiled leader, Khaled Mashaal, lives in Damascus.
Secretary of State Hillary Clinton, in an appearance on Wednesday before the Council on Foreign Relations, said the U.S. was interested in pursuing its engagement efforts in the hopes that "the Syrian conclusion about where they should be positioned with relation to Iran and support for terror activities will be changing."
She also said Washington expected the effort to be "reciprocal." (Read a transcript of Clinton's speech.)
Syria remains a key regional player with influence over events in Lebanon; a close ally of Iran; a crucial border with Iraq; and a significant relationship with Palestinian radical groups.
Washington withdrew Ambassador Margaret Scobey from Damascus in February 2005 to express its "profound outrage" over the assassination of former Lebanese Prime Minister Rafiq Hariri. Syria was the main power broker there at that time.
The Obama administration has decided to return an ambassador to Damascus as a reward for Syria's improved attitude in the region, including the exchange of diplomatic representation with Lebanon and boosting security along its border with Iraq.
By CBS News' George Baghdadi reporting from Sharm el-Sheik, Egypt