2nd round of talks between Russia and Ukraine end with no cease-fire

Peace talks resumed on Thursday between Russia and Ukraine as both sides left the several hours of negotiations without a cease-fire agreement and war continuing to rage.

The Russian and Ukrainian delegations gathered in the Brest region of Belarus for the second round of talks in four days.

"The second round of negotiations is over. Unfortunately, the results Ukraine needs are not yet achieved," Ukraine's presidential adviser, Mykhailo Podolyak, tweeted following the meeting.

Russia's foreign minister said that Russia will continue to insist that any peace agreement with Ukraine must include a promise that Ukraine will "demilitarize." Russia has also signaled it wants to discuss Ukraine adopting a "neutral status" and agree to abandon its ambitions of joining the North Atlantic Treaty Organization (NATO).

Prior to the meeting, Podolyak posted on Twitter that Ukraine's priorities in the talks are an "immediate cease-fire," an armistice and "humanitarian corridors for the evacuation of civilians." Ukrainian officials have previously said they want Russia to withdraw all troops from Ukraine.

Following the meeting, Podolyak tweeted the talks did produce a "solution only for the organization of humanitarian corridors."

During a televised briefing on Thursday with foreign journalists, including ABC News, Russian Foreign Minister Sergei Lavrov said Russia is ready to negotiate.

Lavrov said Russia would continue its military operation while thetalkswere ongoing, saying it cannot allow "military infrastructure" to remain in Ukraine as a threat to Russia.

He said any peace agreement must include a point on Ukraine's "demilitarization."

Zelenskyy on Thursday expressed no interest in demilitarizing and issued a warning to Russian President Vladimir Putin.

"You will repay everything you did against Ukraine -- in full," Zelenskyy said in a televised news conference. "And we will not forget those who perished -- and God won't."

Zelenskyy said he is ready to meet and talk directly with Putin and repeated his calls for a "no-fly" zone over Ukraine immediately, saying it would act as a deterrent.

In an earlier statement posted on Facebook, Zelenskyy said, "We are a nation that broke the enemy's plans in a week" and praised his military forces and Ukrainian civilians who have taken up arms to defend the country.

"I sincerely admire the heroic civilians of Konotop, Bashtanka, Energodar, Melitopol (and) other towns and villages, who do not let the invaders in by blocking the roads. People come out in front of enemy vehicles. This is extremely dangerous. But this is brave. It is also salvation," Zelenskyy wrote.

But when asked at Thursday's news conference by ABC News senior foreign correspondent Ian Pannell how long Ukraine can hold out against the Russian advance, Zelenskyy said, "I don't know."

Putin said in a televised meeting of his National Security Council on Thursday that his "special military operation is going strictly in accordance with the schedule, with the plan."

"All objectives are being successfully attained," Putin said.

As he has done previously, Putin called Ukrainians and Russians "one people" and that his troops are fighting against "neo-Nazis," a claim that has been debunked by the United States and its Western allies.

ABC News' Christine Theodorou contributed to this report.