U.S. President Donald Trump's fresh sanctions on Iran are a "symbolic act" and may leave Washington with no room to exert further pressure on the nuclear power, a former U.S. diplomat said Tuesday.

Trump on Monday signed an executive order to impose "hard-hitting" sanctions on Iranian Supreme Leader Ayatollah Ali Khamenei, whom he said was responsible for the "hostile conduct" of the regime.

While the new sanctions aim to deny top Iranian officials access to important financial resources, "the Ayatollah and most of the people closest to him don't really have bank accounts in their names ... in Europe or outside of Iran" that would be hit by the sanctions, said Amos Hochstein, who served as U.S. special envoy for international energy affairs under the Obama administration.

Washington's new sanctions come on the back of tense U.S.-Iran rhetoric after Tehran downed an American military drone last Thursday. The Trump administration has accused Iran of being responsible for a recent attack on six oil tankers in or near the Strait of Hormuz.

However, Washington may be treading into dangerous waters in its Iran policy, Hochstein told CNBC's "Street Signs Asia."

"When (U.S. Secretary of State Mike) Pompeo says that the United States has sanctioned more than 80% of the (Iranian) economy, that's the good news, but it's also the bad news," he added.

"What else do you have to do that will actually have to affect the Iranians' calculus?" Hochstein asked.