By Nidhi Verma and Douglas Busvine

NEW DELHI (Reuters) - The United States wants India and other countries to wait for a final nuclear deal between Tehran and world powers before actively engaging with Tehran, U.S. Under Secretary Wendy Sherman said on Wednesday.

"I would say 'hold your horses'. We are not quite to an agreement yet," Sherman said, referring to India and other buyers of Iranian oil that want to increase their trade ties with Tehran.

Diplomats are negotiating to fill the gaps in an April 2 framework agreement that would curb Iran's nuclear programme, allaying Western fears it could develop an atomic bomb, in return for relief from international sanctions.

However, the United States has said that further tough negotiations lie ahead and no guarantees that a deal will be secured by a June 30 deadline.

"We understand that nobody wants to be last in line, everybody wants to be first in line, if the sanctions do get relieved," said Sherman, who has been negotiating on behalf of the United States in the long-running Iran nuclear talks.

An Indian delegation recently visited Iran to renew talks on seeking development rights of Farzad B gas field and enhancing oil supplies if a deal is clinched by the end of June.

A delegation-led by Iran's oil minister, Bijan Zanganeh, visited China earlier this month seeking to mend fences with Chinese energy firms to get oil and gas development projects going and discuss oil sales.

Sherman said terrorism and human rights related sanctions against Iran would not be lifted even if a deal was achieved by June 30, indicating that Washington was worried by Iran's influence across the Middle East from Iraq to Lebanon and Syria to Yemen.

Iran-backed Houthi rebels have strengthened their grip over parts of Yemen after seizing the capital Sanaa in September, while Tehran is fighting alongside President Bashar al-Assad's army in Syria's civil war.

"We are still quite concerned about state-sponsored terrorism, we are quite concerned about human rights, we are quite concerned by what is happening in Yemen, what's happening in Syria, other parts of the world, Lebanon," she said.

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Tehran denies any involvement in terrorism.

Sherman said geopolitical events and Tehran's role in them could jeopardize the nuclear talks, but hoped a nuclear deal could be clinched with Iran by the end of June.

"... There are a lot of details that have to be worked out, and there are a lot of events happening in the world, and those events could derail the agreement," said Sherman, who is on an official visit to India.

When asked if the economic sanctions against Iran will be lifted in one stroke after a deal, she said: "It will take some time, even after an agreement, for all the implementation to be worked out".

Iran, which denies seeking nuclear weapons, has said sanctions must be lifted as soon as any final deal is signed.

(Reporting by Nidhi Verma; Editing by Crispian Balmer)