GEOFF BENNETT: Tonight, Russia is attacking Ukraine's capital, Kyiv.

Earlier today, the Kremlin offered a short-term cease-fire in Ukraine, but it wouldn't start for another 10 days.

The U.S., Ukraine and Western European allies have all been pushing Moscow to accept an immediate monthlong cease-fire.

Meantime, Russian forces appear to be slowly gaining ground in areas that could end up as part of a land swap.

Our Nick Schifrin joins us now.

All right, Nick, so what did Russia offer today and what has been the response?

NICK SCHIFRIN: The Kremlin offered a cease-fire that would begin, as you said, Geoff, on May the 8th.

The Kremlin said that it was based on humanitarian grounds.

But May the 9th just so happens to be the day that Russia celebrates the Soviet Union's victory over Nazi Germany in World War II.

You see the images there.

It always includes a big parade in Red Square.

That's from last year.

Now, this year, Chinese President Xi Jinping is scheduled to participate.

And, today, Ukrainian President Volodymyr Zelenskyy said Putin was prioritizing peaceful parades over people's lives.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): For some reason, everyone is supposed to wait for May 8 and only then have a cease-fire to ensure calm for Putin during the parade.

We value people's lives, not parades.

We believe, and the world believes, there is no reason to wait for May 8.

And the cease-fire should not be for a few days, only to resume the killing afterward.

NICK SCHIFRIN: But it wasn't only Zelenskyy today, Geoff, who criticized Putin's proposal.

White House Press Secretary Karoline Leavitt reiterated that President Trump wanted to see the war end, or at least come to a cease-fire, right now.

KAROLINE LEAVITT, White House Press Secretary: He is increasingly frustrated with leaders of both countries.

He wants to see a permanent cease-fire.

I understand Vladimir Putin this morning offered a temporary cease-fire.

The president has made it clear he wants to see a permanent cease-fire first to stop the killing, stop the bloodshed.

And while he remains optimistic he can strike a deal, he's also being realistic as well.

NICK SCHIFRIN: And the reality, Geoff, is that Putin continues to reject the U.S.-European-Ukrainian push for a 30-day monthlong, unconditional cease-fire.

And, instead, continuing today, we see Putin and the Kremlin continuing a maximalist stance on Ukraine.

GEOFF BENNETT: And how are they conveying that position?

NICK SCHIFRIN: So, today, Foreign Minister Sergey Lavrov gave an interview in a Brazilian newspaper.

And he made two key demands.

He -- quote -- "wanted the demilitarization of Ukraine," effectively the end of Ukraine's military, as we know it today, and the denazification of Ukraine.

That is what Russia essentially calls regime change in Ukraine to get rid of President Zelenskyy.

And the Kremlin's statement said that the U.S. had to address -- quote -- "the root causes of the war."

And the Kremlin has clearly identified the root causes as the presence of U.S.-NATO troops in Eastern Europe going back 30 years.

Now, those demands are dead on arrival, not only for Kyiv, but for Western Europe as well.

But those are public positions, Geoff.

And we still do not know to this day what Putin and presidential envoy Steve Witkoff discussed on Friday night in Moscow, nor do we really know what happened at this meeting.

This was President Trump and Zelenskyy meeting in extraordinarily visual statecraft in the Vatican on Saturday.

You heard Karoline Leavitt earlier say that Trump was frustrated with both sides.

But after that pull-aside, Trump actually criticized Vladimir Putin, wondering whether Putin was -- quote -- "tapping me along" and whether Trump would increase sanctions on Russia, which we haven't seen yet.

GEOFF BENNETT: Yes.

Well, as this unfolds, what's happening on the front lines right now?

NICK SCHIFRIN: Moscow certainly claims a level of momentum, especially in Northeast Ukraine.

Let's take a look at the map.

Over the weekend, Russia claimed it recaptured the entirety of Kursk, which Ukraine partially occupied last August.

You see that in blue up top there.

Ukraine says the fighting is ongoing, but it admits it has lost much of what it captured.

Analysts at the Institute of the Study of War, who help us produce these maps, say that as North Korean and Russian soldiers have moved toward that area in Kursk that Ukraine captured, they have turned that into an offensive in the Ukrainian territory of Sumy.

Russia also said that it captured the settlement of Kamianka today.

That is in Kharkiv.

And you saw a video today of Russia flying the Russian flag in that little settlement.

The U.S. proposal actually suggests that, while the U.S. would give de facto recognition to Russian occupation in four territories, it would have to give back territory that you're seeing there that Russia has captured in Kharkiv.

Now, as I just quickly mentioned, Russia says that a lot of the progress that it's made in Kursk is thanks to North Korea.

And, today, for the first time, we saw both Moscow and Pyongyang admit publicly that North Korean troops have been helping.

And you see that video right there, the first video, official video released by Russia showing North Korean troops training in Russia.

Geoff, the suggestion that analysts tell me is that, given the timing of that video and these announcements at this sensitive diplomatic point, that that alliance between Russia and North Korea could well become part of leverage that Russia uses in the peace talks.

GEOFF BENNETT: Nick Schifrin, our thanks to you, as always.

We appreciate it.

NICK SCHIFRIN: Thank you.