Meanwhile, Qatar continued to promote its shuttle diplomacy aimed at ending the seven-month-old war between Iran and the United States.
Trump once again predicted a swift surrender for Iran.
The 26-page letter by the Guards, published on Tuesday, urges Americans to use their political power to remove current leaders from office and reject US support for Israel and military intervention abroad.
While the missive published by Iranian media is unlikely to sway US voters, it identifies issues that US political analysts say are working against Trump and the Republican Party before November 3 congressional elections, when the opposition Democrats could retake control of one or both legislative chambers, potentially impeding Trump's political agenda.
"Remove from power the evil, deceitful and violent politicians who are responsible for America's current state," the letter says.
"Make sure your politicians understand that the world has changed."
Trump campaigned in 2024 pledging to avoid new wars, end existing conflicts and bring down inflation, but the war with Iran, which Trump launched alongside Israel, has contributed to higher global fuel prices and spread in the Middle East.
A Reuters/Ipsos poll published September 21 found just 17 per cent of respondents approved Trump's handling of the cost of living - the top issue Americans say will determine how they vote in November.
Only 34 per cent approved of the strikes on Iran.
Trump allowed the final withdrawal from Iraq on Wednesday, which was agreed in 2024 by former president Joe Biden.
The withdrawal comes 23 years after US-led forces toppled Saddam Hussein, then triggered upheaval that culminated with the rise of Islamic State.
The US war in Iran has drawn in Iranian allies in the region, including the Houthis in Yemen, Hezbollah in Lebanon and militias in Iraq, which Riyadh blamed for the September 10 attack that knocked the East-West Pipeline in Saudi Arabia offline.
The US and Iran have not found an off-ramp from the war despite rounds of talks and several ceasefires.
Negotiations appeared to intensify during last week's UN General Assembly meeting in New York, but have not yielded any agreement to reopen the strategic Strait of Hormuz, through which a fifth of global oil and liquefied natural gas passed before the war started in February.
Qatar has again emerged as would-be peacemaker after previously playing a supporting role in producing a June memorandum of understanding that led to a brief ceasefire.
US and Iranian officials spoke separately with Qatari mediators on Monday, but it was unclear if exchanges took place on Tuesday.
Trump, meanwhile, repeated his position that Iran must not obtain a nuclear weapon and that the war would be over soon.
The conflict has degraded Iran's conventional forces and damaged its already ailing economy, but Tehran has fought back with missile and drone strikes on US allies in the Gulf and by restricting oil tanker traffic in the strategic Strait of Hormuz, which has pushed up world energy prices.
"I don't know if they are going to give up yet but they'll give up," Trump told reporters on Tuesday.
"They are doing very poorly."
At the United Nations General Assembly last week, Iran floated a peace proposal that would trigger a seven-day countdown to reopening the strait and a pause in fighting.
Trump on Saturday rejected the plan although Iranian Foreign Minister Abbas Araqchi said on Sunday that Washington had not officially relayed a US rejection through mediators.
