In a letter published in Jordanian newspapers on Wednesday, King Abdullah urged Prime Minister Bakhit to push through parliament reforms the monarch proposed in February, after the last prime minister was sacked.
Mr Bakhit has branded the IAF's boycott of the local elections as illegal, and this could serve as grounds for action to contest its right to continue to operate as a political party.
In a lengthy interview with the official Petra news agency, Mr Bakhit went on to accuse radical and "immature" elements in the Muslim Brotherhood of seeking to hijack the movement, and take it into dangerous territory.