In his victory address on election night, Barack Obama broke a year-long silence on climate change to warn of “the destructive power of a warming planet.” We are headed back to the United Nations negotiating table.

Hours later, the president’s delegates in the U.N.’s disarmament committee voted to launch a new round of negotiations on a proposed global arms trade treaty. Washington had sidelined those talks in July, for fear the treaty’s provisions might become an issue in the presidential campaign.

After a defensive crouch against conservative attacks in the campaign that he has “subcontracted” American foreign policy to the United Nations, Obama’s election victory has vindicated his commitment to pursue America’s international goals through the world’s sometimes creaky multilateral machinery. And perhaps he can end his second term with the kind of landmark accomplishment that gives concrete reality to his Nobel Peace Prize — awarded to him three years ago simply for abandoning the militarized unilateralism of America’s prior conservative regime.

Obama’s America still rides high in the U.N. arena. In a five-way vote in the General Assembly Monday for three Western seats on the U.N. Human Rights Council, the United States was top vote-getter, comfortably ahead of Germany and Ireland and far outpacing the losing candidates, Greece and Sweden. In President Bush’s first term, Sweden defeated the United States for the human rights commission; in his second term, Bush did not even dare to seek a seat on the council.

Obama’s vote-counting task will actually be harder in Washington, where 67 Senate votes are needed to approve ratification of two long-delayed treaties now considered cornerstones of strengthened peace and security. Here, Democrats’ surprising victories in last week’s Senate elections may embolden Republican colleagues to face down the noisy “black-helicopter” isolationists whose paranoia has paralyzed the ratification process.

The Law of the Sea in particular is widely acknowledged to be a no-brainer, backed by such conservative favorites as the Navy and the U.S. Chamber of Commerce. U.S. non-ratification is especially anomalous given America’s interests in Arctic oil exploration and peaceful resolution of South China Sea territorial disputes. Obama should press for the Senate’s consent to the convention in its lame duck session.

By contrast, the comprehensive nuclear test ban treaty raises substantive concerns on defense policy that justify extensive debate. Its entry into force would constitute a major step toward phasing nuclear weapons out of arsenals and strategic doctrine, and the prospect of its approval understandably agitates supporters of nuclear weaponry. The Senate’s most passionate advocate of the nuclear arsenal, Arizona’s Jon Kyl, is retiring, however, and the test ban should be a second-term priority for the president.

In negotiating a U.N. arms trade treaty, Obama is anxious to defuse American gun owners’ apprehensions. Some important countries harbor their own apprehensions, although China, at least, has shifted on the arms trade treaty along with Obama. Among the 18 U.N. abstentions last week were several countries actively involved in the flow of arms to combatants in Syria’s civil war: Russia, Saudi Arabia, Iran, and Syria itself. They need to be brought aboard the arms trade treaty.

Of course, these countries also need to be brought into a peace process that ends the Syrian war itself. Obama has wisely refused American military support for the rebels, but his administration has pushed the rebel elements to try again to coalesce in a single political front. Whether the new council agreed in Qatar this weekend can hold together is uncertain; the crucial test will be its ability to honor commitments to Washington and the U.N.-Arab League envoy, Lakhdar Brahimi, in their efforts to end the warfare and put Syria’s transition on a political track, underpinned by Security Council unanimity.

The 10 weeks till Obama’s second inauguration also provide the opportunity for him to initiate a new front in the effort to wind down Afghanistan’s 33-year war. Last year, Washington did open America’s first direct negotiating channel with the Taliban insurgency since 2001, but mutual suspicion and Washington’s hesitancy have aborted those talks.

Now is the time to acknowledge that a facilitator appointed by the United Nations may be the last opportunity to bring all the parties to a settlement before the scheduled Western troop withdrawal leaves the Kabul coalition and the insurgency to fight it out on their own. The prospects for harmonizing the interests of Afghanistan’s clashing political forces, its neighbors, and the more distant powers that have supported Afghan reconstruction are uncertain, but trusting simply in a military “solution” after 2014 would truly be a feckless gamble.

Further drift on climate change would be an even more feckless gamble, and the extreme weather events of 2012 have increased recognition in the American public that action cannot be long deferred. In his first year in office Obama signaled his own urgency on the issue by flying to the deadlocked Copenhagen negotiations in hopes personally of breaking the stalemate. He did not achieve the needed breakthrough, and hopes were downsized in successive negotiating rounds.

Global warming was, however, the only international issue he cited in an election-night speech remarkable for its tight American focus. U.N. Secretary-General Ban Ki-moon too, in his congratulatory message to Obama earlier in the evening, urged that climate be a top priority for Obama’s second term, along with Israeli-Palestinian peace.

Having invoked the “warming planet,” Obama now must not fail in addressing it with his global partners. Given the vast network of domestic constituencies and economic as well as environmental issues it raises, climate change is the most complicated but surely the most consequential of issues on the president’s multilateral agenda.

Obama’s conservative foes had sought to portray his commitment to multilateral problem-solving as “weakness,” redolent of the supposed failure of Jimmy Carter. With his second term secured, Obama can easily rebut them: How else but multilaterally can Americans succeed in addressing crises of such global scale as climate, economy, the Middle East, nuclear weaponry, Afghanistan, human rights, and peace?