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From Saad Sayed, Asif Shahzad, and Mubasher Bukhari

Islamabad, April 12 (Reuters) - The United States and Iran failed to reach an agreement to end their war despite lengthy talks that concluded on Sunday in the Pakistani capital, Islamabad, jeopardizing a fragile ceasefire.

Each side blamed the other for the failure of the 21-hour negotiations aimed at ending the conflict that has killed thousands and caused global oil prices to soar since it began more than six weeks ago.

"The bad news is that we did not reach an agreement, and I think that is much worse for Iran than it is for the United States," U.S. Vice President and head of the U.S. delegation told reporters before leaving Islamabad .

America points to "red lines," while Iran sees the demands as "exaggerated."

Vance said, "So we're going back to the United States without a deal. We've made our red lines perfectly clear."

Pakistani sources told Reuters that the American and Iranian delegations had left Islamabad.

Vance said that Iran chose not to accept the American conditions, including not manufacturing nuclear weapons.

He added, "We need to see a strong commitment that they will not seek to acquire a nuclear weapon, and will not seek to acquire the tools that would enable them to quickly make a nuclear weapon. That is the primary objective of the President of the United States, and that is what we have been trying to achieve through these negotiations."

The talks in Islamabad were the first direct meeting between the United States and Iran in more than a decade, and the highest level of discussions since the Islamic Revolution of 1979.

Iran's semi-official Tasnim news agency said that "excessive" US demands had hindered reaching an agreement. Other Iranian media outlets reported that an agreement had been reached on a number of issues, but that the Strait of Hormuz and Iran's nuclear program remained the two main points of contention.

An Iranian Foreign Ministry spokesman said the talks took place in an atmosphere of mistrust. Iranian media quoted him as saying, "It's natural not to expect an agreement in just one session."

Pakistani Foreign Minister Ishaq Dar said it was "essential" to maintain the two-week ceasefire agreed upon on Tuesday, as both sides try to end the war that began on February 28 with US and Israeli airstrikes on Iran.

Israeli security cabinet member Zeev Elkin told Army Radio that further talks were still an option, but warned, "The Iranians are playing with fire."

In his brief press conference, Vance made no mention of reopening the Strait of Hormuz, a narrow waterway through which about 20 percent of the world’s energy supply passes, and which Iran has closed since the start of the war.

Vance said he spoke with US President Donald Trump more than 10 times during the talks.

But even during negotiations on Saturday, Trump said that reaching an agreement was not absolutely necessary.

He told reporters, "We are negotiating. Whether we reach an agreement or not, it doesn't matter to me, because we have won."

The US delegation included Special Envoy Steve Wittkopf and Jared Kushner, Trump's son-in-law. The Iranian delegation included Parliament Speaker Mohammad Bagher Ghalibaf and Foreign Minister Abbas Araqchi.

* Strait of Hormuz

A Pakistani source said of an early round of talks that began on Saturday and continued through the night, "There were fluctuations in the general mood on both sides, and the tension swung up and down during the meeting."

Before the talks began, a senior Iranian source told Reuters that the United States had agreed to release frozen assets held in Qatar and other foreign banks. A U.S. official denied that the release of the funds had been agreed upon.

Iranian state television and Iranian officials have stated that Tehran is demanding control of the Strait of Hormuz, compensation for war losses, a ceasefire across the region, including Lebanon, and the release of assets held abroad.

Tehran wants to collect transit fees through the Strait of Hormuz.

Despite the disputes in Islamabad, shipping data showed that three fully loaded supertankers crossed the Strait of Hormuz on Saturday, the first vessels to leave the Gulf in what appeared to be an earlier ceasefire agreement.

Hundreds of tankers remain stuck in the Gulf, waiting to leave during the two-week ceasefire.

Trump’s stated goals have changed, but he wants at least free passage for international shipping through the strait and restrictions on Iran’s uranium enrichment program to ensure it cannot produce an atomic bomb.

Tehran has repeatedly and for a long time denied seeking to manufacture a nuclear weapon.

Israel continues its bombardment of Lebanon, claiming to be targeting the Iranian-backed Hezbollah group, and insists that these operations are not part of the ceasefire agreement between Iran and the United States. Iran, for its part, insists that military operations in Lebanon must cease.

The Israeli military said it struck Hezbollah rocket launch sites overnight between Saturday and Sunday, and black smoke could be seen rising from the southern suburbs of the Lebanese capital, Beirut, on Sunday. In Israeli towns near the border, air raid sirens sounded, warning of incoming missiles from Lebanon.