"We came to assure you we stood and will continue to stand with the besieged Palestinian people and we will continue with the reconstruction process," he told a news conference.
"The policy of Qatar is to support the people and the official government. We do not support Hamas, we support Hamas as a part of the Palestinian people."
On June 5, Saudi Arabia and its allies severed all diplomatic ties with Qatar, accusing the gas-rich state of bankrolling "extremist" groups, including Hamas.
Islamist movement Hamas has ruled Gaza since 2007 but is considered a terrorist group by the United States, European Union and Israel.
The official Palestinian government is based in the Israeli-occupied West Bank and led by Hamas' rivals Fatah.
Qatar pledged USD 1 billion to reconstruct Gaza after the 2014 war with Israel, the largest single pledge.
Speaking alongside Amadi, Nickolay Mladenov, UN envoy for the Middle East, thanked Qatar for the "commitments you have shown over many years to assist the people of Gaza.