By Jeff Mason

WASHINGTON (Reuters) - The United States urged Tehran on Saturday to "heed the will of the Iranian people" after Iranians elected moderate cleric Hassan Rohani to be their country's next president.

"We respect the vote of the Iranian people and congratulate them for their participation in the political process, and their courage in making their voices heard," the White House said in a statement.

Iran's president runs the economy and wields important influence in day-to-day decision-making, although Supreme Leader Ayatollah Ali Khamenei has the final say on major issues including national security and Iran's nuclear program.

Washington and its Western allies accuse Tehran of pursuing nuclear weapons and have imposed sanctions on Iran that have damaged its economy and triggered a rise in inflation and unemployment. Tehran says its nuclear program is peaceful and aimed at generating power.

In election results announced on Saturday, Rohani scored a surprising landslide victory over conservative hardliners. His resounding mandate could provide some latitude for a diplomatic thaw with the West and more social freedoms at home after eight years of belligerence and repression under President Mahmoud Ahmadinejad.

"It is our hope that the Iranian government will heed the will of the Iranian people and make responsible choices that create a better future for all Iranians," the White House said.

Secretary of State John Kerry said that Rohani "pledged repeatedly during his campaign to restore and expand freedoms for all Iranians.

"In the months ahead, he has the opportunity to keep his promises to the Iranian people," Kerry added in a statement.

The White House said the United States remained ready to engage the Iranian government directly to reach a diplomatic solution to address concerns from the international community about its nuclear program.

But a Middle East analyst said Washington was well aware of the domestic constraints on Rohani's power.

"There's not going to be any quick progress, but from the perspective of the issues the U.S. cares about, this was absolutely the best possible outcome," said Suzanne Maloney, an Iran expert at the Brookings Institution's Saban Center for Middle East Policy.

The White House congratulated Iranians for voting despite difficult security conditions.

"Yesterday's election took place against the backdrop of a lack of transparency, censorship of the media, Internet, and text messages, and an intimidating security environment that limited freedom of expression and assembly," the White House said.

"However, despite these government obstacles and limitations, the Iranian people were determined to act to shape their future."

The election is likely to be a topic of conversation among the Group of Eight industrialized nations leaders at a summit next week. President Barack Obama departs on Sunday for the meeting in Northern Ireland.

Syria - along with Iran's support of President Bashar al-Assad in the civil war there - is expected to dominate the meeting.

(Additional reporting by Jason Lange and Lesley Wroughton; Editing by Will Dunham and Peter Cooney)

[Image: A supporter of moderate cleric Hassan Rohani gestures with a picture of him as she celebrates his victory in Iran's presidential election on a street in Tehran June 15, 2013. REUTERS/Fars News/Sina Shiri]