Gunmen and suicide bombers, acting almost simultaneously, attacked Iran's parliament and a shrine to the revolutionary leader Ayatollah Khomeini in the first attacks in the country claimed by the so-called Islamic State group.

"We grieve and pray for the innocent victims of the terrorist attacks in Iran, and for the Iranian people, who are going through such challenging times," Trump said in a brief statement.

"We underscore that states that sponsor terrorism risk falling victim to the evil they promote."

Earlier, US State Department spokeswoman Heather Nauert said that "the depravity of terrorism has no place in a peaceful, civilized world."

"We express our condolences to the victims and their families, and send our thoughts and prayers to the people of Iran," she added.

Trump has long accused Iran of backing terrorism. During last year's presidential campaign, he suggested that one of his top priorities was to dismantle the "disastrous" 2015 deal aimed at preventing Iran from acquiring nuclear weapons in exchange for the lifting of sanctions.

As president, he has maintained his criticism of Iran -- during a visit to Israel last month Trump said Tehran now feels "emboldened" by the nuclear accord -- but has not tampered with the agreement.

A United Nations watchdog group confirmed in June that Iran was adhering to the deal.

Even as Washington expressed its condolences over the terror strike, the US Senate advanced legislation Wednesday that would impose new sanctions on Iran, partly for what the bill described as the Iranian regime's "support for acts of international terrorism."

Lawmakers voted 92 to 7 to clear a procedural hurdle, setting up a later vote on final passage.

But Republicans and Democrats alike said they are eager to add an amendment that would slap fresh sanctions on Russia in response to US intelligence conclusions that the Kremlin conducted or approved cyberattacks on US targets in an effort to sway the presidential election.

"In the last eight months, what price has Russia paid for attacking American democracy? Hardly any at all," Republican Senator John McCain said.

"We need a strong Russia sanctions amendment. We need it now."

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