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Getting out of the war in Ukraine is elusive

Indeed, even as Russia stepped up its artillery, rocket and bombing strikes on Sunday, Russian and Ukrainian forces were preparing for a decisive battle in Kyiv.

Mr. Putin has demonstrated in past conflicts in Syria and Chechnya a willingness not only to bomb densely populated areas, but also to use civilian casualties as leverage against his enemies. Senior US officials said a protracted battle could ensue in the coming weeks, with thousands of casualties on both sides, as well as among the estimated 1.5 million residents left in the city.

Russian-Ukrainian war: what you need to know

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Iranian nuclear deal. A European Union official said talks to renew the 2015 deal had been suspended following the invasion. Russia, which signed the agreement, tried to use the final approval of the deal as leverage to ease the sanctions imposed because of the war.

Russian and Ukrainian troops are currently engaged in heavy street fighting in the suburbs of the capital, while Ukrainian troops are ambushing the Russians with Javelin anti-tank missile systems supplied by NATO and the United States.

Russian forces vastly outnumber the Ukrainian army and could crush them.

Lieutenant General Scott D. Berrier, director of the Defense Intelligence Agency, told lawmakers last week that there was a limit to how long Kyiv could hold out as Russian forces approached from the east, north and south, tightening the vise. “Because the supply will be stopped, it will become somewhat desperate, I would say from 10 days to two weeks,” General Berrier said.

Another senior US official, speaking on condition of anonymity to discuss confidential intelligence estimates, said it could take Russian forces up to two weeks to encircle Kyiv and then at least another month to capture it. This will require a combination of incessant bombing and street fighting that can last weeks or months.

“There is a very high price to pay in Russian blood for this,” said retired Admiral James G. Stavridis, former Supreme Allied Commander Europe. He added that such a high price could result in Mr. Putin destroying the city with missiles, artillery and bombs, “continuing a series of war crimes that we have not seen in the 21st century.”

The Russian attack has so far failed to achieve any of Mr. Putin’s original goals. But on the battlefield, he’s closer to some targets than others.