The Muslim Brotherhood, which had boycotted the general polls along with other pro-reform groups, said on Thursday that measures taken by King Abdullah II fell far short of true democratic change and that the monarch should not have any say at all in naming a prime minister.
The remarks came after initial results announced by Jordan's Election Commission put the pro-regime loyalists, tribal leaders and businessmen in the lead.
Preliminary figures also show that more than 56 percent of registered voters cast their ballots.
The opposition party dismissed the figure, claiming widespread fraud and vote-buying by wealthy candidates.
"The turnout does not make any sense. They could have done a better job to make people believe," said Zaki Bani Rsheid, deputy head of the Muslim Brotherhood.
"We have closely monitored the electoral process. Vote buying and fake voter cards were very clear. We will prove that our boycott was the right decision," he added.
Jordanians have been holding demonstrations since January 2011, demanding political reforms, including the election of the prime minister by popular vote and an end to corruption.
In October 2012, the Jordanian king dissolved the parliament and called for early elections under growing public pressure. He has also sacked three prime ministers since the start of the popular revolt in the country in a bid to appease protesters.