Iran sent a message to the Biden administration in October saying that it was not trying to kill Donald J. Trump, as Tehran attempted to ease rising tensions with Washington, according to U.S. officials, as well as an Iranian official and an analyst.

The message, sent to Washington through an intermediary, came after a note from the Biden administration in September that warned that the United States would consider any Iranian attempt on the life of Mr. Trump, then the Republican candidate for president, to be “an act of war.”

Since Mr. Trump won the Nov. 5 election, many Iranian former officials, pundits and media outlets have been have been publicly advocating for Tehran to try to engage with the president-elect and pursue a more conciliatory approach, despite vows from Mr. Trump’s allies to renew a high-pressure campaign against Iran.

U.S. officials have said that Iran sought to kill Mr. Trump in revenge for ordering the 2020 drone strike that killed Maj. Gen. Qassim Suleimani, the commander who directed Iran’s militias and proxy forces. The Department of Justice has issued two indictments that officials said were related to Iranian plotting against Mr. Trump.

American officials have also accused Iran of plotting to assassinate other Trump administration figures..

The officials interviewed for this story spoke on condition of anonymity to discuss sensitive diplomatic messages.