The state department said a peace plan outlined by Mr Assad was "detached from reality", calling it "another attempt by the regime to cling to power".
The EU reacted by restating that the Syrian president had "to step aside and allow for a political transition".
The UN estimates that more than 60,000 people have been killed in the uprising, which began in March 2011.
Sunday's televised speech was Bashar al-Assad's first public address since June.
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No sooner did the loud effusive chanting inside the Damascus Opera House subside, than an angry chorus rose from other capitals”
Lyse Doucet
Chief international correspondent
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He denounced opponents as "enemies of God and puppets of the West" and said Syria wanted to negotiate with the "master not the servants".
He said Syria had not rejected diplomatic moves but insisted it would not negotiate with people with "terrorist" ideas.
Mr Assad set out a plan involving a national dialogue conference and a referendum on a national charter.
In Washington, state department spokeswoman Victoria Nuland said the speech was "yet another attempt by the regime to cling to power and does nothing to advance the Syrian people's goal of a political transition".
She added that the initiative "is detached from reality" and undermines efforts by international peace envoy Lakhdar Brahimi.
She repeated calls for President Assad to leave office - as did EU foreign policy chief Catherine Ashton.
"We maintain our position that Assad has to step aside and allow for a political transition," Baroness Ashton's office said in a statement.
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Analysis
James Reynolds
BBC News
The most recent performance advertised on the Damascus Opera House website is for an evening of choral music conducted by the Russian Victor Babenko last May.
President Bashar al-Assad clearly felt capable of commanding the same stage. More than 1,000 supporters were allowed into the main hall to witness his political recital.
Mr Assad repeated the two principal lines of argument that he has employed since the start of the conflict in March 2011 - the opposition is led by foreign terrorists and must be defeated; his own administration is willing to carry out reforms.
The most lasting image from Mr Assad's appearance may come from the moments after his speech. Dozens of supporters surged towards the president - almost prefiguring the frenzy that might happen if the opposition got to him. The president waved,