Britain said Assad's address was "empty" and France said it was an attempt "to justify the repression of the Syrian people".
The office of EU foreign policy chief Catherine Ashton said Europe's position remained that Assad should step down to permit a political transition.
And Egyptian President Mohamed Morsi told CNN he would endorse any decision by the Syrian people to put Assad on trial before the International Criminal Court for war crimes.
The opposition Syrian National Coalition noted that Assad had ruled out any dialogue with the rebels, making negotiations impossible.
Only Iran, which is supplying money, military advisors and, according to the United States, weapons to Assad's regime threw its weight behind its ally.
"The Islamic republic... supports President Bashar al-Assad's initiative for a comprehensive solution to the country's crisis," which rejects "foreign interference," Iranian foreign minister Ali Akbar Salehi said in a statement on his ministry website.
Assad, in his first speech in seven months, on Sunday outlined his vision for a way out of the 21-month conflict that has shattered his country, killed more than 60,000 people according to the UN, and created a well of instability exploited by Islamic jihadists and fuelled by regional rivalries.
Any resolution of the conflict had to be purely Syrian, Assad said -- though he called those Syrians ranged against him "not a loyal opposition but a gang of killers."
He stated that most of the anti-regime fighters were foreigners, and said: "The one thing that is sure (is) that those who we face today are those who carry the al Qaeda ideology."
But while his plan calling for an end to violence, dialogue with opposition elements he deemed acceptable, and a vow to stand fast against those he branded "terrorists" and their foreign backers drew wild applause from his Damascus audience, it offered little realistic prospect of ending what has become a civil war.
'Detached from reality'
"His initiative is detached from reality" and was another attempt "to cling to power," US state department spokeswoman Victoria Nuland said.
British foreign secretary William Hague said the speech was full of "empty promises" and would "fool no one".
"Bashar al-Assad's remarks show once again his denial of reality in which he has shut himself away to justify the repression of the Syrian people," French foreign ministry spokesman Philippe Lalliot said on Monday.
On the day of Assad's speech, another 91 people were killed across Syria, the British-based watchdog the Syrian Observatory for Human Rights said.
Combat continued unabated on Monday outside Damascus, where troops are bombarding rebel positions. Five people, including four members of the same family, were killed in shelling on Kfar Batna to the east, the Observatory said.
In the eastern city of Deir Ezzor, one soldier who had defected was killed in fighting near a local political security branch office.
The United States and Europe, which have declared the National Coalition the "legitimate representative" of the Syrian people, are pressing Assad to leave power as the first step to any process to restore peace in Syria.
But with Russia and China blocking any UN-approved international action against Assad's regime, the Syrian war is slipping ever deeper into bloodshed with fears of lasting sectarian fractures.
Although the toll has climbed sharply in the past six months, and the rebels have grabbed swathes of rural territory, the war has become a grinding impasse punctuated by shelling, regime air strikes and by car bombs set off by an increasingly radicalised insurgency.
Efforts by the joint UN-Arab League peace envoy, Lakhdar Brahimi, have made no more headway than those of his predecessor, Kofi Annan, who resigned in frustration.
Pope Benedict XVI on Monday renewed his call for a ceasefire and dialogue to halt the "endless slaughter" and civilian suffering in Syria.
The conflict, he said, "will know no victors but only vanquished if it continues, leaving behind it nothing but a field of ruins."