"So far the approach on the Israeli-Palestinian issue has been more cautious and more responsible than almost anything else,” Shapiro told Reuters.
"I can’t quite explain why on this one issue they’re closer to the norm than they’ve been on other issues."
Shapiro has gained a following of thousands on his new personal Twitter account, sharing insights gleaned from nearly six years in the Tel Aviv embassy and face-to-face contacts with Prime Minister Benjamin Netanyahu, and correcting misconceptions he perceives on social media about Obama's diplomacy.
In the interview, he said Trump has surprised him by calling for a slowdown in Israeli settlement construction on occupied land Palestinians seek for a state.
The former envoy praised the Republican president's chief negotiator Jason Greenblatt for meeting a cross-section of Israelis and Palestinians during a visit last week that has led to US-Israeli discussions on limiting settlement building.
Still, Shapiro cautioned, Trump's government is inconsistent and unpredictable.
"I’m not sure how comfortable the Israelis should be with an administration that’s hard to read, that’s far from fully staffed, that has a very undeveloped policymaking apparatus and has very divergent voices within it," he said.
On other diplomatic fronts, Shapiro said, the Trump administration has been cozying up dangerously to Russia, backtracking from free trade agreements and international organizations and calling into question Washington's NATO obligations.
When news broke earlier this week that Secretary of State Rex Tillerson planned to skip a NATO meeting, Shapiro pointed on Twitter to a failure to fill staff vacancies.
"That’s OK, he’ll just send his Dep ... I mean, that’s OK, he’ll send the Underse ... I mean, that’s OK, he’ll send an Assistan ... Oh, never mind,” he wrote.
Now an adviser at a hedge fund and a distinguished visiting fellow at Israel's Institute for National Security Studies, Shapiro took the unorthodox course of staying in Israel after leaving his diplomatic post so that a daughter could finish high school exams.
The decision to delay his family's return, Shapiro said in an interview with Reuters, also allows him to avoid what he described as the "bleak" mood in Washington following Donald Trump's election as president.
Shapiro has avoided wading into Israel's domestic politics on Twitter, saying that as a guest in the country, it would be unseemly to do so.
Looking back on the failures of the Obama administration's Israeli-Palestinian peace efforts, he suggested that former Secretary of State John Kerry may have been too idealistic in pursuing talks that collapsed in 2014.
"We might have adjusted our approach had we taken a very realistic assessment whether we had the leadership dynamics to achieve a breakthrough in negotiations,” said Shapiro.
The United States, he said, had been aware after efforts during Obama's first term, of the deep personal mistrust between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas.
"And so it’s a fair question about whether it was realistic at the beginning of the second term that with a concerted effort we could achieve an appreciably different result," Shapiro said.