Exclusive: Australia's former ambassador to Israel says Donald Trump's enforcer-style approach to the two-year conflict between Israel and Hamas earned him enough trust in the region to broker this week's ceasefire.

Trump is being credited locally and globally as the pilot of the peace deal, after 20 living hostages were released from Hamas captivity and hundreds of Palestinian prisoners and detainees were freed on Monday.

Liberal senator Dave Sharma told 9news.com.au Trump was able to achieve a breakthrough peace agreement because he mastered the language of conflict and earned begrudging respect from both sides.

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