Cheney said: "We'll stand with others to prevent Iran from gaining nuclear weapons and dominating this region."
On Saturday, he will make a fence-mending visit to Saudi Arabia.
Riyadh, long a key American ally in the Middle East, recently has spoken out against the US-supported government of Nuri al-Maliki, the Iraqi prime minister, suggesting he is too close to Iran.
Before leaving for Saudi Arabia, Cheney was expected to meet with Sheikh Khalifa bin Zayed Al-Nahyan, the UAE president.
The meeting was expected to focus on pressing Al-Nahyan to support US efforts in Iraq and to shut down Iranian companies in his country that the US believes are backing Iran's nuclear development.
Some 500,000 Iranians live in the UAE.
In Abu Dhabi, Cheney had dinner with Sheikh Mohammed bin Zayed Al-Nahyan, the UAE crown prince .
Cheney's visit comes just two days before Mahmoud Ahmadinejad, the Iranian president, is to visit Abu Dhabi.
Ahmadinejad wants the UAE and other Gulf Arab countries to drop their military alliances with Washington and join Iran in regional efforts.
The US has about 40,000 troops on land bases in Gulf countries outside Iraq and about 20,000 sailors and marines in the region.
No Gulf state has yet backed Iran's offer of an alliance.
In a related development, the UN's nuclear watchdog has denied a report that Iran blocked its inspectors from visiting a nuclear facility where it is enriching uranium.
"There is no truth to media reports claiming that the IAEA was not able to get access to Natanz," Marc Vidricaire, the International Atomic Energy Agency spokesman, said on Friday.
"Iran has a right to pursue nuclear power but it should abide by international agreements and laws"
David, NYC, US
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"We have not been denied access at any time, including in the past few weeks. Normally we do not comment on such reports but this time we felt we had to clarify the matter."
Iran's ambassador to the IAEA also denied the reports.
Last year, Iran held up some inspection visits to Natanz, but access was eventually restored, diplomats familiar with IAEA operations said at the time.