One of the new concepts is a United Nations proposal to “freeze” the fighting on the ground, first in the strategic crossroads city of Aleppo. The other is an initiative from Russia, Mr. Assad’s most powerful supporter, to try to spur talks between the warring sides in Moscow in late January. Diplomats and others briefed on the plans say one Russian vision is of power-sharing between Mr. Assad’s government and some opposition figures, and perhaps parliamentary elections that would precede any change in the presidency.

But the diplomatic proposals face serious challenges, relying on the leader of a rump state who is propped up by foreign powers and hemmed in by a growing and effective extremist force that wants to build a caliphate. Many of America’s allies in the Syrian opposition reject the plans, and there is little indication that Mr. Assad or his main allies, Russia and Iran, feel any need to compromise. The American-backed Free Syrian Army is on the ropes in northern Syria, once its stronghold, and insurgents disagree among themselves over military and political strategy.

And perhaps most of all, the Islamic State controls half of Syria’s territory, though mostly desert, and it has managed to strengthen its grip even as the United States and its allies try to oust it from neighboring Iraq.

Still, Secretary of State John Kerry declared last week that the United States welcomed both initiatives. He made no call for Mr. Assad’s resignation, a notable omission for Mr. Kerry, who has typically insisted on it in public remarks. Instead, he spoke of Mr. Assad as a leader who needed to change his policies.

“It is time for President Assad, the Assad regime, to put their people first and to think about the consequences of their actions, which are attracting more and more terrorists to Syria, basically because of their efforts to remove Assad,” Mr. Kerry said.