Failure to do so, they warned, could awaken a revolt on the scale of those roiling Tunisia and Egypt.
It was a rare rebuke by Jordan's tribesmen, traditional allies of the king and his ruling Hashemite family, signaling that the discontent in Jordan stretches beyond the Islamist and other political opposition movements.
In a letter to Abdullah, 36 tribesmen called for the king to dismiss the parliament elected in November and name a new government to oversee a more transparent election.
They also want changes to an electoral law that critics say allows the king's loyalists to dominate the legislature, the only body in the national government that is elected. And they called for the king to give up his power to choose the Cabinet.
Even before the unrest sweeping Tunisia and Egypt, Jordanians were demanding a greater say in politics and employment opportunities. But protests - most organized by opposition groups, including the Muslim Brotherhood - broke out during the recent unrest around the region.
But the protesters have not called for Abdullah, who marks 12 years since his ascension on Monday, to give up power, suggesting their movement does not pose as dire a challenge to Jordan's ruler.
Like the opposition, the tribesmen also complained of corruption and said those who stole public funds should be held accountable, have their assets frozen and be prohibited from traveling.
That discontent has spread to Abdullah's support base is notable. The tribesmen, or native East Bank Jordanians, hold top positions in the army and security apparatus.
The tribes even rebuked Abdullah's Palestinian wife, Queen Rania, denouncing what they claimed was her overspending and interference in running the country.
"We reject holding birthday parties for persons at the expense of the treasury and the poor," they said in their letter, referring to widespread rumors that the queen celebrated her 40th birthday last August in a lavish gala.
The letter warned that Jordan "will sooner or later face the flood of Tunisia and Egypt due to the suppression of freedoms and looting of public funds."
"We're sounding the alarm because we care for the king and we want the Hashemites to continue to rule us and Jordan," one of the signatories, Ahmed Oweidi Abbadi, said in a telephone interview.
"We're reflecting the views of young Jordanians, whether urban Bedouins or those still living in tents, that the situation has become unbearable, that corruption, nepotism and bureaucracy are widespread and that the rich are becoming richer, while the poor - like many Bedouins - are becoming poorer."
Royal palace officials declined to comment and refused to say if the letter reached the king.
None of the 36 signatories hold any political weight, but their tribal affiliations "make their voices heard," said Labib Kamhawi, a former political science professor at the University of Jordan.
"More and more Jordanians of different political leanings and backgrounds are expected to come out to voice their criticism of the system," he said. "People generally want to keep the king in power, but they're demanding that reforms be enacted immediately."