DUBAI (Reuters) - Iran's elite Revolutionary Guard has warned of the dangers of dealing with U.S. officials, ahead of expected diplomatic contacts, underlining the internal challenges President Hassan Rouhani could face to improve ties with the West.

Rouhani is expected to pursue a charm offensive in the coming week while in New York for the U.N. General Assembly in order to set the right tone for further nuclear talks with world powers which he hopes will bring relief from sanctions, according to diplomats and analysts.

Hours before leaving for New York on Sunday, the new Iranian president said that Tehran was ready for negotiations with Western powers provided they set no pre-conditions. He also said the world needed to accept Iran's right to enrich uranium.

The Islamic Revolutionary Guard Corps (IRGC) military force was established to safeguard Iran's revolution in 1979 and has since influenced political, social and economic affairs.

"Historical experiences make it necessary for the diplomatic apparatus of our country to carefully and skeptically monitor the behavior of White House officials so that the righteous demands of our nation are recognized and respected by those who favor interaction," an IRGC statement said.

It added the IRGC would support initiatives that were in line with national interests and strategies set forth by Iran's theocratic leader and highest authority, Ayatollah Ali Khamenei.

The United States and its allies have imposed tough economic sanctions on Iran over suspicions Tehran intends to develop a nuclear capability. Iran says the program is purely peaceful.

The IRGC statement, published by Iran's Tasnim news agency on Saturday and marking the 33rd anniversary of the start of the Iran-Iraq war, came days after Khamenei and Rouhani told the security hardliners to stay out of politics, in effect instructing them not to scupper the new centrist government's attempt to resolve the nuclear dispute.

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The 125,000-strong IRGC has a military budget that is said to dwarf that of the regular armed forces. Its top commanders are handpicked by Khamenei but its clout also derives from former members who have occupied positions of influence in business, parliament and across provincial government.

Rouhani spoke about negotiations with the West when addressing the military parade on Sunday to commemorate the annual "Sacred Defence Week".

"In these talks all the rights of Iran, including nuclear and enrichment rights on our own territory should be accepted within the framework of international law," he said, according to state news agency IRNA.

Rouhani also paid homage to Iran's armed forces and indicated that the country would not forget about the suffering former Iraqi President Saddam Hussein imposed on Iran, and his backing from Arab and western states.

Iranian television showed footage of the parade featuring Sajjil and Ghadr missiles which commanders claim have a range of about 2,000 km (1,200 miles). Media reports said the latest air defence systems were also showcased.

"Our armed forces do not aim to dominate and colonize the region but in the face of aggression they will not dither and will defend the independence and the honor of our country and revolution with all their might," Rouhani said.

U.S. President Barack Obama and his aides have made clear that they are ready to test Rouhani's intentions to seek a diplomatic solution to the nuclear dispute.

The White House has left open the possibility Obama and Rouhani could meet on the sidelines of the U.N. meeting, and a U.S. official has privately acknowledged the administration's desire to engineer a handshake between the two leaders, which would be the highest-level U.S.-Iranian contact since the 1979 Islamic Revolution.

Last week, Khamenei appeared to give his strongest endorsement yet to Rouhani's attempts to initiate talks with the United States, saying he agreed with "heroic flexibility".

Reflecting optimism over Rouhani's diplomatic initiative, Iran's currency, the rial, has strengthened against the dollar by more than six percent. Open-market traders currently offer around 29,000 rials to the dollar versus 31,500 a week ago.

(Reporting by Marcus George; Editing by Pravin Char and Mark Potter)