In the letter of designation, King Abdullah directed Razzaz and his yet-to-be-formed team to launch a comprehensive national reform scheme that seeks to "empower the Jordanian people" and enable them to realise their potential and meet their needs and demands.
Shops and pharmacies closed in Jordan's capital on Wednesday as some unions pressed ahead with a strike protesting against tax hikes, after King Abdullah replaced his prime minister to try to defuse public anger.
The government's priority, His Majesty said, is to stimulate economic growth, enhance the country's competitiveness and create jobs for the youth.
The king said the new cabinet should review the tax system and immediately start a dialogue over the draft income tax law, which protesters have staunchly opposed.
Harvard-educated Omar al-Razzaz, seen here on the left, has been tasked with forming a new government in a bid to appease the protesters.
Jordan, which has a peace treaty with Israel, has navigated years of instability at its borders, including wars in Iraq and Syria and conflict in the Israeli-occupied West Bank.
Despite Mulki's resignation, daily street protests continued, with organizers saying they would not quit until the tax bill has been scrapped.
A draft law to raise income taxes and International Monetary Fund-driven reforms that have pushed up prices have sparked the country's largest protests in years.
He also said political parties, unions and civil society groups must take part in the talks.
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Thousands rallied in the Jordan's capital pushing nationwide protests into its fifth consecutive day.
"We want to change the path, not the individuals", he said.
Amman's massive street protests showed no signs of stopping despite Mulki's resignation on Monday.
Many demonstrators said they wanted more than Mulki's departure. Mr Mulki also said it was up to parliament to decide whether to passed it or not.
King Abdullah attributed the political and economic crisis which has led to protests to the country bearing the burden of hosting Syrian refugees despite the decline in worldwide aid, and accused the global community of failing to fulfil its duties towards Jordan.
Since January, resource-poor Jordan, which suffers from high unemployment and poverty, has seen repeated price rises including for staples such as bread, as well as extra taxes on basic goods.
Officials say Razzaz had been an opponent of reforms that hurt the poor.
Another, who gave his first name as Khalil, said Jordan's political system, which grants the monarchy vast executive powers, should become more democratic and accountable.