"We will never give up the right to launch a peaceful satellite, a legitimate right of a sovereign state and an essential step for economic development," a foreign ministry spokesman told the official KCNA news agency.
The spokesman was responding to Obama's comments Sunday and Monday during a visit to South Korea.
The US leader said his country was not hostile to the North's people but denounced the rocket launch scheduled between April 12-16.
The US and other countries say it would in fact be a long-range missile test banned under UN resolutions.
"The US head of state said he had no hostile intention towards us," the spokesman said.
"But if that remark is genuine, he should abandon the confrontational mindset that tries to block us, and should have the courage to admit that we have as much right to launch our satellite as other countries do."
The North said it would judge whether Obama's remarks disavowing hostility were genuine "or just another hypocrisy" depending on whether his country applies a double standard to the satellite launch.
It said it had invited foreign experts including those from the US National Aeronautics and Space Administration (NASA), along with overseas reporters, to witness "a scientific space technology project that has nothing to do with any military purpose".
Obama has said any launch would jeopardise a US-North Korean deal reached only last month, under which the North agreed a partial nuclear freeze and a missile test moratorium in return for US food aid.
The North insists its satellite launch is not a missile test.
There was no reason to conduct such a test at this time "after labouring so much to reach an agreement with the US and when the whole political atmosphere is favourable", it said.
A satellite launch to mark the 100th anniversary of the birth of founding president Kim Il-Sung had been ordered by his son and successor Kim Jong-Il, it said.
Jong-Il died in December and was succeeded by his own son Jong-Un.
South Korea also fiercely opposes the launch, saying it is intended to test technology to deliver a nuclear warhead.
"If North Korea pushes ahead, it will pay for what it has done," said Unification Minister Yu Woo-Ik.
The exercise seemed to be part of North Korea's strategy to be recognised eventually as a nuclear-armed state, he said.
While the North's foreign ministry statement was measured, the country's Uriminzokkiri website took sharper aim at Obama's trip, which began Sunday with a visit to the tense inter-Korean border.
The US leader peered into the North through binoculars and told US troops the contrast between the two Koreas could not be starker.
Uriminzokkori, in a editorial dated Monday and seen Tuesday, said Obama made his "provocative and violent remarks" while North Koreans were holding memorial events marking the 100th day since Kim Jong-Il's death.
The US leader "viciously defamed our sacred passion to commemorate the leader", it said.
"This is another indication of the extreme anti-North aggression dominating Obama's mind and such disrespectful provocation against our 100th day of mourning can never be tolerated," it added.