On Sunday, Haniya confirmed he had accepted Hamas's nomination and said: "I pray to God to help me to shoulder this great responsibility ... to serve the Palestinian cause until the return of the Palestinian rights."
Haniya, 43, is widely viewed by Palestinians as a pragmatist who has forged good relations with rival factions.
Hamas crushed the long-dominant Fatah faction in the parliamentary election on 25 January.
The group presented Haniya's candidacy to Abbas, the Palestinian president, on Sunday, paving the way for talks on forming a government.
Hamas has said it hopes to persuade other parties to join a national unity administration in negotiations that could take several weeks.
Speaking to reporters at his house in the Beach refugee camp, Haniya said he and other leaders would meet Abbas later in the day in Gaza "to take the first steps" towards forming a government.
"We will engage in dialogue and everything will be on the table for discussion," he said.
At the opening session of the Hamas-led parliament on Saturday, Abbas urged a future Hamas government to recognise past peace deals with Israel and commit itself to pursuing statehood through talks. Hamas rejected that call.
"We will engage in dialogue and everything will be on the table for discussion"
But Haniya said: "We want to avoid any sharp debate, especially while the [Israeli] occupation refuses to recognise Palestinian rights and refuses to recognise the agreements signed with the [Palestinian] Authority."
Elected under the slogan of Change and Reform, Haniya said the group would seek to introduce political, social, economic, financial and administrative reforms into authority institutions plagued by corruption.
Commenting on the possible cut-off or reduction of Western aid to a Hamas-led government, Haniya said the group had several alternatives.
"We have our Arab and Islamic nations and we have also some countries in the international community which expressed a desire to have relations with the coming government."
Haniya told Aljazeera on Sunday: "Hamas will bear its responsibilities on both the Palestinian and regional levels.
"Palestinians are looking forward to a government reflecting their ambition, expressing their hopes and sticking to their rights and objectives.
"Hamas will be open to the regional and international community. Hamas has to preserve and serve its people's rights and maintain their economic and security requirements," he told Aljazeera.
In Jerusalem, the Israeli cabinet said it was cutting off the monthly transfer of tax revenues that Israel collects on behalf of the Palestinian Authority and urged international donors to stop all but humanitarian aid.
Haniya said the Israeli restrictions were aimed at "bringing the Palestinian people to their knees".
"These decisions do not frighten our Palestinian people and they do not frighten the coming Palestinian government. We had dealt with challenges in the past and we will be able to handle the coming challenges."