King Abdullah becomes first Arab ruler to call for Syria's president to resign after eight months of uprising.
The king made the comments in an interview with the British Broadcasting Corporation (BBC) on Monday, two days after the Arab League voted in favour of suspending Syria's membership over its crackdown on anti-government protests.
The Cairo-based regional bloc has given Syria until November 16 to halt the crackdown or face implementation of the suspension in an apparent closing of ranks among Arab states against the government in Damascus.
"I believe, if I were in his shoes, I would step down," Abdullah said. "I would step down and make sure whoever comes behind me has the ability to change the status quo that we're seeing."
Jordan has been critical of its northern neighbour's crackdown on anti-government protesters in recent months, which the United Nations estimates has killed at least 3,500 people since March.
King Abdullah, the first Arab ruler to issue such a call over the eight months of uprising, said Assad should usher in a new era of political dialogue before stepping down.
"Again, I don't think the system allows for that, so if Bashar has the interest of his country, he would step down, but he would also create an ability to reach out and start a new phase of Syrian political life," he told the BBC.
Damascus had no immediate public comment.
'Conspiring against Damascus'
Al Jazeera's correspondent Nisreen El-Shamayleh, reporting from the Jordanian capital, Amman, said: "This is a turning point in Jordan's position in what is happening in Syria; in recent month government officials have shied away from making any strong statements about Syria.
"Syria and Jordan have never enjoyed the friendliest of relations. In the last few decades they were always marred with tension. and nobody knows what triggered this kind of response.
El-Shamayleh said Jordan's cabinet would meet on Tuesday to discuss how the country would do its part to implement Syria's suspension from the Arab League. Our correspondent said the withdrawal of Jordan's ambassador in Damascus appeared to be imminent.
Fawaz Gerges, director of the Middle East Centre at the London School of Economics, said that despite the king's comments, the reality wass that Assad "is not going anywhere".
"The Syrian response, I suspect, would be that the Arab counterparts have no right to preach to them about democracy and respect for human rights because the Arab counterparts are not born-again democrats," he told Al Jazeera.
"What King Abdullah said - and this is very surprising for many people - it tells you about the extent of divisions within the Arab League and among the Arab states. There seems to be a consensus emerging among Arab states that President Assad must go. The Americans had made the argument a few days ago."
Syria has reacted angrily to the Arab League's threatened suspension. Walid al-Moallem, Syria's foreign minister, on Monday accused Arab nations of conspiring against Damascus, calling Saturday's near-unanimous vote at the Arab League's headquarters in Cairo, "shameful and malicious".
European Union governments also agreed on Monday to extend sanctions against Syria to 18 more individuals associated with Assad's violent crackdown on dissent.