UNITED NATIONS -- Russia's foreign minister pummeled the Trump administration's policies this week, calling U.S. threats "destabilizing" and ultimatums regrettable, but at the U.N. on Friday Sergey Lavrov offered more of an olive branch to the White House. Asked by CBS News about U.S. leadership in global conflict zones, the Kremlin's top diplomat said, "In today's world, the leadership can only be a collective thing ... we need collective efforts."

"Such a powerful country as the U.S. can indeed do a lot of beneficial things in eliminating terrorism," Lavrov said. "We are interested in coordinating our actions."

Lavrov went on to say that there is a channel between militaries on Syria and that interaction has helped avoid the establishment of the Islamic State of Iraq and Syria, or ISIS, as a caliphate.

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But on the Iran nuclear deal, Lavrov was less forgiving. Russia's top diplomat said that the deal cannot survive if the U.S. pulls out of the accord.

Russian Foreign Minister Sergei Lavrov attends his annual news conference in Moscow, Russia, Jan. 15, 2018. Reuters/Sergei Karpukhin

Last week, President Trump said there were "disastrous" flaws in the 2015 agreement but waived implementing nuclear-related sanctions, saying, "This is a last chance." The Trump administration has threatened that the deal must be changed within the next four months or Washington will withdraw.

Lavrov told reporters on Friday, "This agreement cannot be implemented if one of the participants unilaterally steps out of it. It will fall apart; there will be no deal then."

Richard Gowan, associate fellow at the European Council on Foreign Relations, told CBS News, "Iran is an issue that unites almost everyone other than Israel against the U.S. at the U.N. Russia will take every opportunity to drive wedges between the U.S. and the Europeans over the Iranian nuclear deal."

As Russia appears to be taking the lead in some areas of global leadership, Lavrov warned the U.N. Security Council to avoid "zero sum" approaches to world affairs. After meeting with Syria's U.N. ambassador, Lavrov told reporters that the U.S. attempt to establish local forces in northern Syria contradicts a commitment to maintain the country's territorial integrity.

The U.S. and Russia have sparred frequently in recent months on Syria after Russia vetoed a Security Council vote on a U.S.-sponsored resolution to extend the mandate of chemical weapons inspectors. France's Ambassador Francois Delattre has announced a meeting scheduled for Tuesday in Paris of countries that want to end impunity for the chemical weapons attacks in Syria, a move supported by the U.S.

"I see Russia as a canny tactical player at the U.N., and Moscow has won big over Syria," Gowan said.

Just as Lavrov was speaking at the U.N. and to reporters, U.S. Ambassador Nikki Haley distributed a letter, obtained by CBS News, to the 15-member Security Council on the Russian position on Syria's chemical weapons, pointing to over a dozen "false" and "misleading" statements by Russia on the issue.

Meanwhile, Secretary of State Rex Tillerson's deputy, John Sullivan, spoke to the Security Council on Afghanistan while Haley, a Cabinet member, was in Washington to meet with the president's national security team.

A Security Council diplomat emerged from the Afghanistan meeting saying that, with Trump administration policies being contested, Russia has "enhanced its power worldwide."

Other U.S. allies are trying to mend broken fences with Russia. U.K. Foreign Secretary Boris Johnson said last month, "The Kremlin has positioned Russia in direct opposition to the West, but it doesn't have to be that way."

And, on the controversial decision of the Trump administration to cut funding to the U.N. Relief and Works Agency for Palestinian refugees, Russia has stepped in.

Regarding the Israel-Palestinian conflict, Lavrov said that Russia never shied away from being a broker in the peace process: "We saw there was interest from Israel and Palestine, and we suggested that (Israeli Prime Minister Benjamin) Netanyahu and (Palestinian President Mahmoud) Abbas meet in Russia without preconditions."

Lavrov lamented what he called "Russophobia" in the U.S. but said he was confident it would pass and that the U.S. has a vested interest in improving relations.

"And how these or other actions of the U.S. on the global arena are seen, well, you probably will draw your own conclusions." he said.