Saudi television showed Abdullah receiving Cheney in the desert town of Tabuk in the far north of the kingdom. Cheney was coming from the UAE where he visited a US aircraft carrier in the Gulf.
He was due to leave for Cairo later on Saturday.
US military resolve
Cheney said on Friday that heightened US military presence in the Gulf demonstrated Washington's resolve in a standoff with Iran over Tehran's nuclear plans.
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"Iran has a right to pursue nuclear power but it should abide by international agreements and laws"
David, NYC, US
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Saudi Arabia shares US concerns about Iran's nuclear programme, which Teheran says is only for civilian purposes.
But Saudi Arabia and its Arab allies - Egypt and Jordan - want Washington to press Iraq's Shia-led government into a new political deal with Sunni Muslims.
They are concerned about US troops leaving Iraq before such an agreement is brought forward.
In turn, Washington wants Arab countries to do more to help stabilise the government of Nuri al-Maliki, Iraq's prime minister.
Cheney's trip follows on from last week's conference on Iraq at the Egyptian resort of Sharm al-Sheikh.