In an interview with Fox Business on Saturday, Trump spoke about the correspondence.
"There are two ways Iran can be handled: militarily, or you make a deal", to prevent Tehran from acquiring nuclear weapons.
At a meeting with senior Iranian officials, Khamenei said Washington's aim was to "impose their own expectations", Iranian state media IRNA reported.
"The insistence of some bullying governments on negotiations is not to resolve issues," he said.
"Talks for them is a pathway to have new demands, it is not only about Iran's nuclear issue. Iran will definitely not accept their expectations," Khamenei was quoted as saying, without directly mentioning Trump.
"Some foreign governments and boorish personalities are pushing for negotiations, but their goal is not to solve problems. Rather, they seek to use negotiations to get their own way and impose their demands," the 85-year-old said, according to IRNA.
In response to Khamenei's comments, White House National Security Council spokesman Brian Hughes reiterated almost word for word the choice of negotiations or military action that Trump said he had presented to Iran.
"We hope the Iran regime puts its people and best interests ahead of terror," Hughes said in a statement.
While expressing openness to a deal with Tehran, Trump has reinstated a "maximum pressure" campaign that was applied during his first term as president to isolate Iran from the global economy and drive its oil exports to zero.
During his 2017-2021 term, Trump withdrew the United States from a landmark deal between Iran and major powers that had placed strict limits on Tehran's nuclear activities in exchange for sanctions relief.
After Trump pulled out in 2018 and re-imposed sanctions, Iran breached and far surpassed those limits.
UN nuclear watchdog chief Rafael Grossi has said that time is running out for diplomacy to impose new restrictions on Iran's activities, as Tehran continues to accelerate its enrichment of uranium to near weapons-grade.
The 2015 nuclear deal formally expires in October.
Tehran says its nuclear work is solely for peaceful purposes.
Khamenei, who has the last say on Iran's key policies, said there was "no other way to stand against coercion and bullying".
"They are bringing up new demands that certainly will not be accepted by Iran, like our defence capabilities, missile range and international influence," he was quoted as saying.
Although Tehran says its ballistic missile program is purely defensive, it is seen in the West as a destabilising factor in a volatile, conflict-ridden Middle East.
Tehran has in recent months announced new additions to its conventional weaponry, such as its first drone carrier and an underground naval base amid rising tensions with the US and Israel.
with dpa
