It had previously said that it would bar listings in those areas.
Last year, the hospitality company had announced plans to remove Jewish settler homes in the occupied West Bank from its rental listings, saying that it took this decision to end lawsuits brought against it by the hosts.
"We're hopeful that we have some ideas that are different, unique, which will allow the Israelis and the Palestinian people to come to a resolution of the conflict", Pompeo said. "I will call Chris Lehane and congratulate him for doing it and urge him to make sure he keeps it".
As part of its agreement with the plaintiffs, Airbnb issued a statement disavowing the Boycott, Divestments and Sanctions (BDS) movement, which has sought to convince companies and celebrities to boycott Israel in a manner similar to boycotts against South Africa in the 1980s.
Airbnb didn't comment beyond its blog post announcing the change.
"Airbnb's reversal demonstrates why we can't just rely on companies to take the right decisions, and that we need governments to fulfil their obligations by intervening and passing laws obliging their companies to respect human rights". We want to keep our journalism open and accessible and be able to keep providing you with news and analysis from the frontlines of Israel, the Middle East and the Jewish World.
Sarah Stern, Endowment for Middle East Truth founder and president told JNS that Tuesday's decision "is a tremendous victory against the prejudicial and discriminatory policies of the BDS movement" and that "other companies who have chose to support the BDS movement would be wise to take heed".
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Most world powers view Israel's construction of settlements on occupied land as a violation of global law, and Palestinians say it is wrong for companies to profit from them.
The announcement came after Israeli lawyers filed a class action lawsuit on behalf of property hosts and others, following the decision previous year by Airbnb that it would remove such listings. The movement to boycott Israel saw the decision as a victory.
During the course of the almost 52-year Israeli military occupation, more than 50,000 Palestinian homes and structures have been demolished, and tens of thousands of Palestinians have been forcibly removed.
Because of the pending litigation Airbnb had not implemented the announced policy, and now that the litigation has been settled the policy will never be implemented and the property owners have been saved from suffering any losses.
Mort Klein, president of the Zionist Organization of America, said that the decision was a "necessary and important retraction".
The plan to eliminate the listings of Airbnb had been hailed by some groups like Human Rights Watch.
He had done so while expressing hope that Airbnb would drop its policy, which now has happened. "We also welcome their clear rejection of BDS and embrace of the Israeli market", said ADL CEO Jonathan Greenblatt.