Haniya said "resistance in all its forms" was a "legitimate right" in the speech setting out the programme of his new government.
"The government will work with the international community to put an end to the occupation and recover the legitimate rights of our people," he said.
The government would attempt to build a Palestinian state on the lands occupied by Israel in 1967, Haniya said.
The coalition government would also attempt to reach a prisoner exchange deal with Israel, the senior Hamas leader said.
In his earlier speech, Abbas had called for a negotiated peace with Israel and a rejection of "all forms of violence".
The Palestinian president also urged Western powers lift their international boycott of the Palestinian Authority.
They have demanded that the Palestinian government recognise Israel, renounce violence and abide by previous peace agreements.
"The government will win an easy vote of confidence," Salah al-Bardaweel, spokesman for Hamas's parliamentary bloc, said on Friday.
But it remains to be seen what effect, if any, the coalition government between rival Hamas and Fatah has on international relations.
The new government is likely to pledge "respect" for past Palestinian-Israeli agreements, in line with a Saudi-brokered agreement reached by Hamas and Fatah in Mecca on February 8.
Following Haniya's speech, Israel re-iterated its position that it would not deal with the incoming government.
"This is just a ploy to regain international hand-outs with smoke and mirrors"
LeotheIsaurian, Detroit, US
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Miri Eisin, a government spokeswoman, said: "Israel will not recognise or work with this new government or with its members."
"And not only is there no renunciation of terrorism, there is a clear call by the new prime minister to what he calls the right of resistance.
"We expect the international community to firmly stick to its demands concerning the three conditions."
Ziyad Abu Amr, Palestinian foreign minister in the new administration, told Al Jazeera that the unity government was willing to talk to Israel.
"This is a unity government not a Hamas government. We are ready to deal with the Israelis if they are ready."
Israel has urged foreign powers to continue the financial boycott imposed a year ago after Hamas defeated Fatah in an election and formed a government.
Ahead of the vote, a US official told Reuters news agency that Washington would leave the door open to contacts with Salam Fayyad, finance minister-designate, who is not from Hamas, but would not deal with him in his official capacity.
Britain seemed to take up a similar position with a senior diplomat saying contacts would be made with non-Hamas ministers.
"Britain is not going to have contact with Hamas, but there are members of the government who are not Hamas and British diplomats will be able to have contact with them," the diplomat told Reuters.
Amr Moussa, the secretary-general of the Arab League, criticised the British decision.
"If this reaction is true, I say it's a very negative one," Moussa told reporters in Tunis, adding that the unity government was a positive move which would be backed by the Arab world.
France and Russia have been more positive about the unity government, the former inviting Ziad Abu Amr to visit Paris.
"Hamas rejects the selectivity in dealing [with] the ministers of the government of national unity. We urge Britain and all European countries to reconsider the position from the incoming government," Ismail Rudwan, a Hamas spokesman, said.