Sinwar made the remarks in a meeting with Palestinian youths in Gaza earlier on Thursday to talk about the implementation of the recent reconciliation deal Hamas signed in Cairo with Fatah.
"The United States reiterates the importance of adherence to the Quartet principles: any Palestinian government must unambiguously and explicitly commit to nonviolence, recognize the State of Israel, accept previous agreements and obligations between the parties - including to disarm terrorists - and commit to peaceful negotiations", the statement said.
"This is blatant interference in Palestinian affairs because it is the right of our people to choose its government according to their supreme strategic interests", said senior Hamas official Bassem Naim.
Hamas has been in complete political and military control of the Gaza since it seized control of the Strip from Abbas's Fatah party, which dominates the Palestinian Authority, in a bloody battle in 2007.
Greenblatt said Hamas must meet the worldwide demands to recognize Israel and accept previous agreements with it. Hamas "must accept these basic requirements" to take part in government, he said.
Israeli Education Minister and Jewish Home chairman Naftali Bennett welcomed Greenblatt's statement, saying the American administration had sent a clear sign to both Israelis and Palestinians. Hamas leader Yehia Sinwar has rejected such demands, declaring in Gaza: "The time in which Hamas discusses the issue of recognizing Israel is over".
"I am pleased that President Trump's envoy, Jason Greenblatt, made it very clear that Hamas must be disarmed, Israel must be recognized and previous worldwide decisions must be honored", Netanyahu said.
On Tuesday, Israeli Prime Minister Benjamin Netanyahu said his government would refuse any diplomatic talks with the unity government if Hamas had any role in it.
"We are ready to cut a deal that would also include the release of the leaders of several Palestinian factions now held by Israel", he said. In an official statement, the government said that "as in the past, we continue to hold the position that the government of Israel will not conduct negotiations with a Palestinian government that depends on the inclusion of a terrorist group that seeks the destruction of Israel".
The agreement led to the creation of the Palestinian Authority, an interim self-governing body meant to lead to an independent Palestinian State on the territories of East Jerusalem, the West Bank and the Gaza Strip, which Israel occupied in 1967.