In the letter appointing Mr Razzaz to form a new government on Tuesday, King Abdullah said that the cabinet "must carry out a comprehensive review of the tax system" to avoid "unjust taxes that do not achieve justice and balance between the incomes of the poor and the rich".
Jordanians have taken to the streets of the country's capital an several other cities to protest an IMF-backed draft income tax law and price hikes.
The kingdom has experienced an economic downturn in part because of prolonged conflict in neighboring Syria and Iraq, and a large influx of refugees several years ago. He will be succeeded by Omar Razzaz, the Harvard-educated education minister.
Late Monday, the king had warned Jordan was "at a crossroads", blaming the economic woes on regional instability, the burden of hosting hundreds of thousands of Syrian refugees and a lack of global support. Jordan's unemployment rate stands at 18.4 percent, according to government statistics.More news: NASA reveals new discoveries suggesting there was once life on Mars
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"We want new people who really want to bring in reforms, we do not want politicians from the same circles who only want to solve the IMF's problems by stealing money from the people's pockets", one male protester, who declined to give his name, told AFP.
Public anger has grown over government policies since a steep general sales tax hike earlier this year and the abolition of bread subsidies, both measures driven by the International Monetary Fund. Mr Mulki also said it was up to parliament to decide whether to passed it or not. "The individuals (in government) do not concern us if they change, we want to change the approach of the government", said Ali al-Abous, head of the Professional Unions Association. Razzaz had previously held senior positions in the World Bank and is considered a reformer.
Protest organizers have said they seek real change, including a rescinding of the tax bill, and that personnel changes at the top are irrelevant without fundamental reforms. His appointment nevertheless sends a message to foreign donors that Jordan will press ahead with reforms, though in a gradual way, they said.
The government says it needs more funds for public services and argues that the tax changes reduce social disparities by placing a heavier burden on high earners.
Demonstrators say a new tax bill backed by the International Monetary Fund will hurt the poor and middle class.