AMNA NAWAZ: Welcome to the "News Hour."

Russian President Vladimir Putin today responded to a U.S.-Ukraine offer for a temporary cease-fire with his own demands and questions about what a 30-day pause in the war would mean for his long-term ambitions in Ukraine and Europe.

Putin is meeting with President Trump's envoy, as Ukraine says that Putin's words show he is not ready for peace.

Nick Schifrin begins our coverage.

NICK SCHIFRIN: Tonight, a high-stakes negotiation between Russian President Vladimir Putin and U.S. envoy Steve Witkoff, after Putin today said a cease-fire must answer his demands.

VLADIMIR PUTIN, Russian President (through translator): We agree with the proposals to stop the fighting, but we believe this cessation should be one that would lead to long-term peace and eliminate the initial causes of this crisis.

NICK SCHIFRIN: The Kremlin has long translated initial causes as the presence of U.S. and NATO troops in Eastern Europe.

Congressional officials tell "PBS News Hour" the Trump administration had already been considering reducing U.S. troops in Europe.

The Kremlin has also demanded Ukraine refuse NATO weapons, cap its military size and abandon NATO membership.

Those are red lines for Ukraine, but the Trump administration appears willing, at the very least, to block Ukraine's NATO ambitions.

Today, Putin also disparaged the very idea of a temporary pause.

VLADIMIR PUTIN (through translator): How will these 30 days be used, for Ukraine to continue forced mobilization, so that the mobilized units are trained?

How can we be guaranteed that nothing like this happens?

NICK SCHIFRIN: Today, Russian troops regain the largest town in the Russian region of Kursk, parts of which have been occupied by Ukraine since last summer.

Putin said any cease-fire would first have to answer Kursk's fate.

VLADIMIR PUTIN (through translator): If we stop fighting for 30 days, what does this mean, that everyone who's there will go out without a fight, that we must release them from there, or the Ukrainian leadership will give them a command to lay down their arms, to surrender themselves?

How will this be?

It's unclear.

NICK SCHIFRIN: In the White House with NATO Secretary-General Mark Rutte today, President Trump described Putin's initial reply as positive.

DONALD TRUMP, President of the United States: We are getting good signals outside of Russia as to where we are with Russia, and hopefully they will do the right thing.

NICK SCHIFRIN: And President Trump reiterated his desire to stop the war as quickly as possible.

DONALD TRUMP: He put out a very promising statement, but it wasn't complete.

And, yes, I'd love to meet with him or talk to him.

But we have to get it over with fast.

NICK SCHIFRIN: But, today, Putin demanded more answers and appeared in no rush.

VLADIMIR PUTIN (through translator): Who is going to give orders for the cessation of hostilities?

Who will determine where and who has committed a violation of the cease-fire?

These are all questions that require painstaking research on both sides.

There are some issues we should discuss, maybe with President Trump.

NICK SCHIFRIN: Tonight, Zelenskyy said Putin was not ready for peace.

VOLODYMYR ZELENSKYY, Ukrainian President (through translator): That's why in Moscow, they are surrounding the cease-fire idea with such preconditions that it either fails or gets dragged out for as long as possible.

Now is the time to increase pressure on him.

Sanctions must be applied.

DONALD TRUMP: You don't have the cards right now.

NICK SCHIFRIN: But, publicly, President Trump's pressure has been on Zelenskyy personally and on Ukraine by halting military aid and pausing intelligence sharing for six days.

In private, administration officials tell "PBS News Hour" that president ordered sanctions on Russia to be more tightly enforced.

And he has, at times threatened more sanctions.

But, today, he held back.

DONALD TRUMP: I do have leverage, but I don't want to talk about leverage now, because right now we're talking to him.

And based on the statements he made today, they were pretty positive, I think.

NICK SCHIFRIN: But the man who started this war also made it clear today there is no deal until his questions are answered and his demands are met.

For the "PBS News Hour," I'm Nick Schifrin.