"Undoubtedly, the American people are not satisfied with this behaviour and they showed their discontent in the recent elections," Ahmadinejad wrote.
"I hope that in the wake of the mid-term elections, the administration of President Bush will have heard and will heed the message of the American people."
"If the US government meets the current domestic and external challenges with an approach based on truth and justice, it can remedy some of the past afflictions and alleviate some of the global resentment and hatred of American.
"But if the approach remains the same, it would not be unexpected that the American people would similarly reject the new electoral winners, although the recent elections, rather than reflecting a victory, in reality point to the failure of the current administration's policies."
Ahmadinejad wrote a rambling, 18-page letter to Bush in May, which Washington criticised for not addressing Iran's nuclear programme.
The US is leading the drive to impose UN sanctions on Tehran for its refusal to stop enriching uranium.
Wednesday's letter made no mention of Iran's nuclear programme.
Iranians in the street were disappointed by the cold response to the May letter because, while it did not make clear proposals, it was the first official communication between the two countries' presidents since the Islamic Revolution of 1979.
Earlier this month, Ahmadinejad said he was planning to write a letter to Americans.
In Wednesday's letter, he focussed on past good relations between the US and Iran and between their peoples who are both "inclined towards the good, and towards extending a helping hand to one another, particularly to those in need," and who deplore "injustice, the trampling of peoples' rights and the intimidation and humiliation of human beings."
The Bush administration is opposed to Tehran's
Ahmadinejad has alienated many Americans by calling for Israel's destruction and repeatedly dismissing the holocaust as a myth.
He also strongly supports the Palestinian group Hamas and the Lebanese faction Hezbollah, which the US State Department lists as terrorist organisations.
In Wednesday's letter, he said, "we, like you, are aggrieved by the ever-worsening pain and misery of the Palestinian people" and accused the Bush administration of disregarding public opinion by remaining "in the forefront of supporting the trampling of the rights of the Palestinian people."
"What has blind support for the Zionists by the US administration brought for the American people?," Ahmadinejad asked.
"It is regrettable that for the US administration, the interests of these occupiers supersedes the interests of the American people and of the other nations of the world."
He urged Americans to support the right of the Palestinians to live in their own homeland.
Growth of terrorism
He said that the US invasion of Iraq, while overthrowing Saddam Hussein which people "are happy about", has led to hundreds of thousands of deaths, an exponential growth of terrorism, and no rebuilding of Iraq's ruined infrastructure.
"I consider it extremely unlikely that you, the American people, consent to the billions of dollars of annual expenditure from your treasury for this military misadventure.
"Now that Iraq has a constitution and an independent assembly and government, would it not be more beneficial to bring the US officers and soldiers home, and to spend the astronomical US military expenditures in Iraq for the welfare and prosperity of the American people?
As you know very well, many victims of Katrina continue to suffer, and countless Americans continue to live in poverty and homelessness."