In an interview in Doha, Khaled Meshaal told CNN's Nic Robertson the Trump administration has a "greater threshold for boldness" than its predecessors.
"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."
The Hamas leader's comments come as Trump meets Palestinian Authority leader Mahmoud Abbas Wednesday at the White House, as the US president works toward what he's called the "ultimate deal" between Israel and the Palestinians.
Efforts by previous US administrations have focused on a two-state solution, but at a February press conference with Israeli Prime Minister Benjamin Netanyahu at the White House, Trump told reporters
, "I'm looking at two-state and one-state, and I like the one that both parties like ... I can live with either one."
Meshaal said the release of a new Hamas policy document Monday handed Trump the chance to break from the failures of previous administrations to achieve a deal.
"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 said.
In the new policy document
, Hamas -- for the first time -- indicated the group was willing to accept the idea of a future Palestinian state falling within borders that existed in 1967, before Israel took control of the West Bank, Gaza and east Jerusalem.
The area defined by 1967 borders is widely recognized by the international community as the site of a future Palestinian state, sitting alongside the state of Israel, in a so-called "two state" solution.
Meshaal said that Hamas -- considered by the US and others to be a terrorist organization -- had adopted the stance in order to create a "unified political position" with its rival Fatah movement, which currently controls the West Bank and the Palestinian Authority.
It was also seeking to win support from various Arab states and the wider international community.
Hamas stopped short of recognizing Israel in its policy document, stating there would be no "compromising its rejection of the Zionist entity and [no] relinquishing [of] any Palestinian rights."
Meshaal echoed the sentiment, telling CNN: "Israel doesn't recognize Palestinian rights. When Palestinians have their own sovereign, free state then they can choose without outside pressure."
Meshaal called on Trump to exercise pressure on Israel's "intransigence" when it comes to settlements and its occupation of the West Bank. He said this was "key" to arriving at a "real and equitable peace in the region."
In February, for the first time in about 20 years, Israel announced it would build a new settlement in the West Bank.
New homes have been built in the past, but were additions to existing settlements.
Israel responded to the document's release by accusing Hamas of attempting to dupe the international community.
"Hamas is attempting to fool the world but it will not succeed," said David Keyes, a spokesman for Israeli Prime Minister Benjamin Netanyahu.
"Daily, Hamas leaders call for genocide of all Jews and the destruction of Israel. They dig terror tunnels and have launched thousands upon thousands of missiles at Israeli civilians. Schools and mosques run by Hamas teach children that Jews are apes and pigs. This is the real Hamas," he said.
'Daily acts of aggression'
The Hamas leader said Israel's land and sea blockade of the Gaza strip, and its occupation of much of the West Bank, were acts of "daily Israeli aggression."
As such, he insisted that Hamas's launching of rockets on Israel were acts of "resistance, not violence."
When asked if Hamas was willing to stop its rocket attacks and smuggling of weapons through tunnels, Meshaal said the group would not "abandon what little it has to defend itself."
Israel has maintained its blockade of the Gaza Strip since 2007. Israeli officials say it is needed to stop the Palestinians from launching rockets on Israeli cities -- which have killed civilians -- and to prevent Hamas, which runs the strip, from obtaining new weapons.
The blockade has been criticized by the United States and various international organizations.
But not all Palestinians see Hamas's move as the conciliatory gesture Meshaal is touting it as.
At the Doha press conference that unveiled the new policy document, Meshaal was flanked by two large screens with a live video stream from Gaza city. A lavish ballroom in Doha's Sheraton hotel contrasted rather uncomfortably with the press room in Gaza that would sometimes become plunged in darkness by a power cut.
Ironically, it was the Gaza crowd that wasn't up for Hamas's new compromise. "We want liberation and not negotiation," said one activist. "This document is a contradiction," yelled out another, and it is a sentiment that is so far being echoed across the conflict's wide political divide.