"I would like to inform you that your maintenance of the ceasefire is an absolute Palestinian interest and will be for the benefit of the people of Gaza and of course Hamas, which seized control of the strip," Rice was quoted by Ma'an, a Palestinian news agency, as saying.
"I would also like to commend the measures you have taken to protect the borders with Israel and prevent extremist terrorists from launching rockets at the south of the Jewish state," the message continued.
"I feel it is important for Hamas to be ready to renounce terrorism and to seriously consider living peacefully in two states, side by side in peace and security, allowing both the Israeli and Palestinian sides to live in peace and prosperity.
"I hope this can be the beginning of greater communication with Hamas, after your assimilation into the negotiation process and acceptance of the Quartet committee's demands."
'Recognition of Hamas'
Abu Marzouk said that Hamas considers the message a "recognition" of its existence, although the US still labels Hamas as a "terrorist" organisation.
Ahmed Youssef, a senior political adviser to Ismail Haniyeh, the deposed Palestinian prime minister and a key Hamas member, told the Al Ahram newspaper that the message does not herald a massive change in the current relationship between Hamas and the US.
"It certainly reflects the US administration's sense that the justifications upon which it has long grounded its antagonism towards Hamas and the Palestinian resistance are crumbling," he said.
According to Al Ahram, a source in the Haniyeh government said that communications have been taking place for more than a year between his government and the office of Tony Blair, the Quartet's Midde East envoy.
Mahmoud al-Zahar, the former Palestinian foreign minister from Hamas, confirmed that Hamas had received a message from Rice.
But "this cannot be regarded as a turning point in relations between the US administration and Hamas", he said.
Odeh said these messages are not new.
"Previous US administrations have constantly tried to nudge isolated political parties into mainstream politics," she said.
"It also indicates that the US government cannot deny the influence of Hamas in the region."