The letter from Mahmud al-Zahar also referred to a "two state solution" for the Middle East conflict, an outcome that would require recognition of Israel, a state which the the Islamist group denies has a right to exist.
"We are looking for freedom and independence side by side with our neighbours and we are ready for serious discussions with the Quartet," said a copy of the letter to Kofi Annan, the UN chief, obtained by AFP on Tuesday.
The Quartet of the European Union, Russia, the UN and the US are the sponsors of the stalled Middle East peace process and the drafters of the road map seeking to create a Palestinian state alongside Israel.
"We look forward to living in peace and security, as all countries in the world, and that our people enjoy freedom and independence side by side with all our neighbours in this holy place," the text added.
Hamas, whose first government was sworn in last week, has in the past carried out scores of suicide bombings in Israel and is officially committed to armed struggle to end Israeli occupation of Palestinian territories.
Its charter calls for the destruction of Israel and the establishment of a Palestine on land today incorporated in modern Israel.
Yet the copy of the letter seen by AFP referred to the "two-state solution" to the Middle East conflict and said the Hamas-led government was committed to opening peace talks with the international community.
"Israeli procedures in the occupied territories will put an end to all hopes to reach a final settlement based on the two-state solution," it said.
Despite a sweeping poll victory,
Hamas is facing an uphill task
An official in al-Zahar's office in Gaza City, where the Hamas leader is based, denied that the letter included any sense of recognising Israel or its right to exist.
"Zahar sent a letter to Annan but he did not recognise Israel or make any mention of anything related to Israel's right to exist," he said.
Al-Zahar's letter reiterated previous calls from Hamas for peace talks with the international community, although it has refused to renounce violence, explicitly recognise Israel or previous peace agreements.
"Our government is serious about working with the Quartet," it said.
"Our government is ready for serious discussions and to work with the United Nations and with the entire international community to strengthen security, sovereignty, peace and independence in our region based on just resolutions."