"The Syrian authorities are going to exercise all their influence over Hezbollah and over the various actors" in the conflict, Mr Moratinos said after meeting with President Bashar al-Assad and other senior officials.
However, he told reporters, Syrian leaders want a "change in the circumstances and the political-military context in which Lebanon lives."
An unnamed Syrian official, quoted by the official SANA news agency, later denied that Mr Moratinos had made such comments and dismissed them as having "no basis."
Syria and Iran are accused by the West of financing and arming Hezbollah, but Damascus claims it provides the group only with moral support.
Mr Moratinos, a former EU Middle East envoy who had travelled to Beirut and Damascus to press efforts by Brussels to end the fighting, said his visit to Syria had achieved its objectives.
He had asked Syria "to be constructive in this very delicate situation we are facing and I received a positive answer from the Syrian authorities.
"Syria wants to be part of the solution. Syria doesn't want to be part of the problem."
In particular, he said he and the Syrians had agreed a common position on a French proposal calling for an immediate ceasefire and the subsequent deployment of an international peacekeeping force.
Lebanese Prime Minister Fuad Siniora has appealed to his British counterpart Tony Blair to push for an immediate ceasefire in the conflict between Lebanon's Hezbollah and Israel.
In an interview with BBC television, Mr Siniora said "right now Tony Blair can call for an immediate ceasefire," which would pave the way for a broader mutual agreement.
However, Mr Blair and US President George W. Bush back Israeli demands for political and security guarantees before a ceasefire can take place.
Following a ceasefire, Mr Siniora said his government will work to imposeorder nationwide and help Israel get back its captured soldiers if Mr Blair and other leaders press Israel to withdraw from occupied territory and return prisoners.
US Senate resolution
Meanwhile the US Senate has passed a resolution demanding Syria and Iran halt their aid to the Hezbollah militant group, and called for a cessation of hostilities in Lebanon.
The non-binding resolution called on Tehran and Damascus to "end all material and logistical support for Hezbollah," and urged the two countries to "use their significant influence over Hezbollah to disarm the group."
The measure, approved by a voice vote, called the hostilities betweenHezbollah and Israel "a threat to the peace and security of the peoples of Israel and Lebanon," and called for an end to the fighting.
International force
Up to 10,000 Israeli ground troops are battling Hezbollah around more than a dozen villages in south Lebanon establishing a six to eight kilometre buffer zone between Israel and Hezbollah fighters.
The difficulty of assembling such an international buffer force was highlighted when the United Nations postponed for the second time a meeting of countries that might contribute troops.
France issued a new draft United Nations resolution on the crisis, but amid prolonged talks with the United States expressed pessimism about hopes for Security Council action on the conflict before next week.
Differences between France and the United States also forced the United Nations to again postpone the planned meeting on the international force.
US President George W. Bush and German Chancellor Angela Merkel have discussed UN efforts to get a Middle East truce and a multinational force for Lebanon, the White House said.
"She offered her help and support in dealing with interested parties," and the two leaders also discussed Iran and Syria, spokesman Tony Snow said.
Washington remains "pretty optimistic" about getting a UN Security Council resolution calling for an end to fighting between Israel and Hezbollah and the deployment of a multinational force, said Mr Snow.
"I can't give you an absolute timeline, if it's going to be this week or the beginning of next week," said the spokesman, who called the diplomatic wrangling "a matter of days."
With the West in diplomatic disarray, Iranian President Mahmoud Ahmadinejad, whose country is a staunch supporter of Hezbollah, told a Muslim summit: "The real cure for the conflict is elimination of the Zionist regime, but there should be first an immediate ceasefire."
The summit of the 57-nation Organisation of the Islamic Conference demanded an immediate truce, with Malaysian Prime Minister Abdullah Ahmad Badawi telling delegates: "Muslims are angry even in moderate Muslim countries."
New York-based rights group Human Rights Watch issued a report branding some Israeli attacks on Lebanese civilians as "war crimes", and said it was wrong to blame the high death toll on Hezbollah fighters using civilians as shields.
The UN force in south Lebanon said the Israeli army is holding positions in seven different locations in Lebanese territory after launching two new ground incursions.