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Hamas leader Khaled Meshaal has called on US President Donald Trump to find an "equitable solution" for Palestinians and break with past US approaches to the Middle East peace process.

Meshaal's comments came as Trump met Palestinian Authority President Mahmoud 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 civilised world and the American administration to stop the darkness that we have been suffering from for many years."

Meshaal pointed to a policy document released Tuesday by Hamas that for the first time shows a willingness to accept the idea of a Palestinian state within borders that existed after the 1967 Israeli occupation.

"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.

While the new document does not amount to recognition of Israel, it formally softens its stance in a few key areas. The new charter drops anti-Semitic references and redefines the enemy as the "Zionist project" rather than the Jewish faith.

"Israel doesn't recognise Palestinian rights. When Palestinians have their own sovereign, free state then they can choose without outside pressure," he told the broadcaster.