The Asian Development Bank (ADB), a multilateral lender dominated by the United States and Japan, says it will selectively support coal-based power projects if cleaner technologies and other safeguards are adopted. Last year, it approved a $900 million loan to help build a 600 megawatt coal-fired plant in Pakistan.
The articles of agreement of the AIIB, which will include its lending strategy, will not be finalized until the end of 2015, Chinese officials have said.
Kim said he understood India's position on coal-fired energy projects, but the World Bank's stand would not change.
"We have to be sensitive to the fact that climate change is something that, India for example, has contributed much less to than the United States or Europe or other countries and what they're saying is, that we need energy," he said.
Read MoreChina to again levy coal import tariffs after nearly a decade
"And what they're saying is: that we need energy now so that our economies can grow, so that we can provide jobs for our people," he said.
"Now we won't be engaged in coal unless there's absolutely no other option, and we'll see where they go," Kim said.
Signed up despite rivalry
India signed up late last month to be a founder-member of the AIIB, and is also a member of a new development bank from the BRICS group of emerging markets - Brazil, Russia, India, China and South Africa. The cooperation comes despite traditional rivalry - the two Asian giants fought a brief war in 1962 and have overlapping territorial claims along their Himalayan border.
The Indian official, who was involved in the AIIB decision, said the funding of infrastructure in the region by the World Bank and the ADB was inadequate.
Read MoreUS opposing China's answer to World Bank
"Had the World Bank resourced its capital base, had the World Bank done reforms that are due, and ADB also resourced the capital base, perhaps there would have been no need to set up the (new) bank," the official said.
Experts say the Asia-Pacific region needs about $1-1.5 trillion per year to fund infrastructure needs. The World Bank's total lending to East and South Asia was about $16.6 billion last year. At the end of 2013, the ADB's lending amounted to $21.02 billion, including co-financing with other development partners.
"The infrastructure financing gap in Asia, in emerging Asia, is so big and even the existence of ADB, World Bank, and other multilateral development banks cannot fulfill that demand," Indonesian Finance Minister Bambang Brodjonegoro told Reuters last week. "AIIB will be a welcome newcomer."
The AIIB was launched at a ceremony in Beijing at which 21 nations were represented, but Australia, South Korea and Indonesia were absent. Australia and South Korea were pressured not to join by the United States, local media in both countries said, but Indonesia said it did not attend because its new government had not taken office.
Read MoreIndonesia Q3 GDP grows at slowest pace in 5 years
On Tuesday, Brodjonegoro said Indonesia could join the AIIB as early as next week.
Analysts say Washington's fears about the AIIB are that the new bank will encroach on its role in providing funds to the region through Western-backed institutions and that it will allow China to assume leadership in Asia.
"Don't imagine for a moment that the AIIB is just about economics," said Hugh White, professor of strategic studies at Australian National University.
"Asia really does need more infrastructure and there does need to be some new funding mechanisms, but it's also an opportunity for China to build its political and strategic leadership role in Asia."