President Obama declared himself hopeful about the prospects of slowing climate change Tuesday, even as he acknowledged that the actions emerging from the United Nations climate summit here would fall short of the desired international targets.

“I’m optimistic. I think we’re going to solve it,” Obama said during a 47-minute news conference capping a two-day visit to the gathering. “The issue is going to be the pace and how much damage is done before we’re fully able to apply the brakes.”

Citing “the old expression that necessity is the mother of invention,” he said, “Well this is necessary.”

Obama has spent more than a year helping to lay the groundwork for the summit, persuading countries to pledge to cut ­greenhouse-gas emissions, although agreement on a final text is not complete.

Over the next 10 days, negotiators must work out differences over financing arrangements, transparency and the scope of certain countries’ commitments. Agreement to make actions and plans transparent have to be a binding part of the Paris deal, Obama said.

Moreover, if the ambitious plans set forth here are to become a crowning legacy for Obama, they must be enlarged in future years, climate experts say. Obama said he believes that changes in technology — and regular international reviews of climate plans — will make it easier to make larger cuts.

The president pointed to the commitment rolled out Monday by billionaire Bill Gates, Microsoft’s co-founder, and other wealthy people to invest in technology that could slow climate change.

“What gives me confidence that progress is possible is someone like Bill Gates who­ . . . understands that tackling climate change is not just a moral imperative but an opportunity,” Obama said. “That kind of optimism, that kind of sense that we can do what is necessary, is infectious.”

Brushing off congressional Republicans’ threats to block requests for new international funding for the Green Climate Fund and to undo the Clean Power Plan that is central to Obama’s carbon-reduction strategy, the president said it was “just part of the games that Washington plays.” He said that even if a Republican succeeded him as president — something he said he does not expect — the gravity of his or her role would alter their posture toward climate science.

“You are not just playing to a narrow constituency back home, but you are in fact at the center of what happens around the world,” he said.

For all his proclaimed optimism, Obama has put aside one policy he said made sense: a carbon tax. Many countries — including Germany and Japan — support such a tax because it would alter incentives and could provide a steady stream of revenue to fund other investments or renewable technologies.

“I have long believed that the most elegant way to drive innovation and reduce carbon emissions is to put a price on them,” he said. “This is a classic market failure.”

But because of opposition to such a tax in Congress, he has not proposed one.

Obama’s optimism also came in contrast to frustrations in many island nations and other countries most vulnerable to climate change. The president met a small group of those leaders — including Kiribati President ­Anote Tong, whose entire country could be submerged by the Pacific Ocean — in a lavish dining room at the U.S. ambassador’s residence here Tuesday morning.

Obama pledged support to island nations whose existence is threatened by climate change, citing his childhood in Indonesia and Hawaii with the declaration: “I am an island boy.”

“Their populations are among the most vulnerable to the ravages of climate change,” the president said after meeting with several of the island nations’ leaders.

“Some of their nations could disappear entirely, and as weather patterns change, we might deal with tens of millions of climate refugees in the Asia-Pacific ­region,” he added.

But Obama did not alter the administration’s opposition to “loss and damage” payments from major economies based on historical emissions, and he did not budge on demands from island nations that the Paris agreement aim to limit global warming to 1.5 degrees Celsius instead of 2 degrees.

He said, however, that the United States would support the island nations, and the administration said Monday that it would give the world’s poorest nations $52 million to deal with climate change. And the White House also announced that it would contribute a total of $30 million to insurance-risk pools in Africa, Asia and the Caribbean.

“These nations are not the most populous nations. They don’t have big armies,” Obama said. “But they have a right to dignity and sense of place . . . and their voice is vital in making sure that the climate agreement that emerges here in Paris is not just serving the interest of the most powerful.”