Despite US pressure on countries to weaken ties with Iran,the UAE, a US ally, remains Iran's largest trading partner.
Bilateral trade is said to stand at $11.7bn in 2007, with imports from the UAE forming the bulk of the exchanges at $9.2bn.
Dubai serves as a hub for Iranian business despite a longstanding dispute between the UAE and Iran over three strategic Gulf islands.
Parviz Davoudi, Iran's first vice-president, said: "We talked about different issues including the economy and both countries emphasised the expansion of economic ties."
He also said that al-Maktoum stressed "Iran's right to peaceful nuclear activities".
The West fears Iran could use atomic technology to make an nuclear bomb but Tehran insists it only wants electricity.
Mahmoud Ahmadinejad, the president, is trying to boost Iran's relations with Arab states. Last May, he made the first visit by an Iranian leader, post-revolution, to the UAE.