Khaled Meshaal's comments came as Trump was due to receive Palestinian president Mahmud Abbas at the White House to explore avenues for reviving the deadlocked peace process.
Interviewed by CNN in Doha, Meshaal said Trump has "greater threshold of boldness" than previous US administrations.
"This is a historic opportunity to pressure Israel ... To find an equitable solution for the Palestinian people," he said. "And it will be to the credit of the civilized world and the American administration to stop the darkness that we have been suffering from for many years."
"This is a plea from me to the Trump administration -- the new American administration -- break out from the wrong approaches of the past and which did not arrive at a result. And perhaps to grab the opportunity presented by Hamas' document," Meshaal told CNN.
The Hamas document stopped short of recognizing Israel, however, and Hamas for years has called for its destruction.
"Israel doesn't recognize Palestinian rights. When Palestinians have their own sovereign, free state then they can choose without outside pressure," he said in the CNN interview.