Jordan faces a contracting economy after several years of robust growth.
The boom was supported by strong foreign direct investments, including remittances from a large skilled workforce in the Gulf Arab region.
The new cabinet line-up is likely to continue Jordan's free market reforms that critics accuse of deepening the divide between rich and poor, officials told the Reuters news agency.
They said Abdullah will count on Rifai to win support for his economic and social reforms among the conservative establishment, the backbone of the king's power base.
His father, Zeid Rifai, the current speaker of the upper house of parliament, was prime minister several times in the 1970s and 1980s.
In the designation letter, King Abdullah instructed the new prime minister to form a government that would have the primary aim of arranging new general elections, saying the ballots should not be held later than the fourth quarter of 2010.
"The elections should represent a qualitative transition in Jordan's democratic march and presents the kingdom as a model in transparency, fairness and impartiality," the monarch said.
He also directed Rifai to amend the controversial election law and to take all necessary steps that ensure the participation of all citizens in the polling process.