The resolution, tabled by ruling Pakistan People's Party lawmaker Shahnaz Wazir Ali, was passed by treasury and opposition members of the National Assembly or lower house.
Besides expressing concern at Obama's backing for India's bid, the resolution said the balance of power in South Asia would be affected if India is given such a status.
Talking to reporters at Lahore airport, Foreign Minister Shah Mahmood Qureshi expressed similar concerns, saying India's bid for permanent membership of the UNSC "would have a negative impact on balance of power in the region".
India cannot become a member of the UNSC only with the support of the US as the move must be backed by a two-thirds majority in the world body, Qureshi said.
"Pakistan's opposition to India's move is in line with its stance regarding expansion and reforms in the world body," he said, adding "We are of the view that any unilateral support, if it is not based on deep thinking, would affect the peace and stability of the region."
Qureshi said Pakistan is not opposing India's bid "just for the sake of opposition but we have reasons for it".
The expansion and reform of the UN Security Council is a long-drawn and complicated process with groups comprising countries of different regions having divergent viewpoints on the issue, he observed.
Referring to Italian Foreign Minister Franco Frattini's comments in this regard during a news conference in Islamabad yesterday, Qureshi said the reform of the UNSC could not be achieved by having more permanent members.
Replying to a question about China's stance on India's bid, Qureshi said the issue was discussed with China and both countries had a unanimous stand in this regard.
"China is a responsible state and always uses decent diplomatic language while reacting on international issues and we are satisfied with its stance," he said.
There is national consensus on the issue and the cabinet had already passed a resolution expressing apprehensions about India's bid to become a permanent member.
Qureshi said the US has the right to develop bilateral relations with India and this would not affect its ties with Pakistan. Islamabad has been an ally of Washington for many years and Obama's support to India would not affect Pakistan-US relations, he added.
Meanwhile, a copy of resolution passed by the Pakistani Cabinet was handed over to UN Secretary-General Ban Ki-moon by Pakistan Mission at the United Nations.
