WASHINGTON—The State Department said Iran’s support for terrorism was “undiminished” in 2014, and the U.S. remains very concerned about the activities of Iran’s Revolutionary Guards and its proxies in the Middle East.

The U.S. worries about Iran’s activities were included in an annual report of global terrorism between 2013 and 2014, released Friday.

Of particular concern, the report said, was Iran’s continued support of the powerful Hezbollah militia and political party in Lebanon; and its assistance to fighters supporting Syrian President Bashar al-Assad’s regime. Iran also hasn’t identified or initiated judicial proceedings against senior al Qaeda leaders it has in custody.

The release comes less than two weeks before a June 30 deadline for a deal on limiting Iran’s nuclear program. U.S. officials say those talks are separate from any destabilizing activities in the region by Tehran.

“We think it’s essential that we pursue those negotiations,” said Tina Kaidanow, the State Department’s coordinator for counterterrorism. “None of that implies that we would be, again, in any way taking our eye off the ball with respect to what Iran is doing as a supporter of terrorism.”

She said sanctions on Iran related to terrorism would remain in place even if a nuclear deal is reached.

The report said “Iran’s state sponsorship of terrorism worldwide remained undiminished” in 2014 and Ms. Kaidanow said the U.S. continued to be “very, very concerned” about its activities, adding that Tehran hasn’t changed its behavior this year.

The U.S. and five other world powers are negotiating with Iran to curtail its nuclear program in exchange for sanctions relief. Critics of the deal fear Iran will funnel funds it gains access to into supporting terrorist activities.

President Barack Obama told The Atlantic magazine last month that Iran supports terrorism despite the current sanctions, and that its leaders will be under pressure to improve the Iranian economy.

More broadly, the report found that global terror attacks surged 35% between 2013 and 2014 and the violence caused deaths to jump more than 80%. That came on top of a 43% increase between 2012 and 2013.

Last year’s report connected the increase to the rise of aggressive al Qaeda affiliates while this year’s sources the surge to Islamic State and the conflict in Syria.

The State Department report said nearly 33,000 people were killed in almost 13,500 terror attacks around the world last year. It attributed the surge in deaths in part to attacks that were “exceptionally lethal,” including 20 attacks that killed more than 100 people compared with two on that scale in 2013. In 2013, there were 9,707 terrorist attacks that killed more than 17,800 people.

The increase in global terror attacks follows Islamic State’s unprecedented seizure of territory in Iraq and Syria and the continued prevalence of weak or failed governments in Yemen, Syria, Libya, Nigeria and Iraq.

More than 9,400 people were kidnapped or taken hostage in terrorist attacks in 2014, three times as many as in 2013. Most of the kidnappings occurred in Iraq, Nigeria and Syria.

The report also pointed to troubling trends in the flow of foreign fighters to Syria and Islamic State’s use of social media to attract recruits as well as communicate with local Sunni Arab populations. Though Islamic State has begun to form relationships with affiliates beyond Iraq and Syria, it is unclear if those contacts are simply opportunistic or more significant, the report said.

Lone wolf terror attacks are becoming an increasing concern, the report found, pointing to killings in Quebec and Ottawa last October and Sydney last December. As Western nations have increased border security, groups like al Qaeda and Islamic State might increasingly rely on inspiring “lone actors” to wage attacks.

The report said the threat of core al Qaeda decreased in 2014 as the group continued to lose leaders and Islamic State touted itself as a leader of a global movement. Still, al Qaeda continues to inspire affiliates like AQAP in Yemen, the Nusra Front in Syria and al-Shabaab in North Africa to carry out attacks.