President Sheikh Khalifa has sent a message of congratulations to Kazakhstan's new prime minister, Alikhan Smailov.
Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, and Sheikh Mohamed bin Zayed, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the Armed Forces, delivered similar messages to Mr Smailov on his appointment.
The veteran politician was nominated by Kazakh President Kassym-Jomart Tokayev before being voted in by MPs.
Mr Smailov, 49, served as first deputy prime minister in the previous cabinet, which Mr Tokayev dismissed last week following violent clashes in the country.
Kazakhstan's security forces have detained 9,900 people over the unrest, in which more than 160 people were killed, the Interior Ministry said.
Mr Tokayev has called the unrest an attempted coup and said that his security services would never shoot peaceful protesters.
Sheikh Mohamed bin Zayed talked to Mr Tokayev on Monday, expressing his wish to see peace in the Central Asian country.
In a phone call, Sheikh Mohamed said the Emirates supported everything that could help to achieve stability.
Mr Tokayev briefed Sheikh Mohamed on the latest developments and the measures taken to establish security and to protect Kazakhstan's institutions.
Sheikh Mohamed expressed his confidence in the ability of the government and people in Kazakhstan to quickly overcome this difficult period.