Ukraine will send a delegation on Wednesday to meet with Russia for a second round of talks aimed at stopping the fighting, a spokesman for Ukraine President Volodymyr Zelenskyy has told ABC News.

Russia earlier announced it was sending a delegation to sit and wait for possible talks but that Ukraine had not confirmed it would talk part in the negotiations.

Ukraine and Russia held talks on the Belarus-Ukraine border two days ago but without a breakthrough, according to officials.

Ukraine's foreign minister Wednesday morning said it was ready to negotiate but not to accept Russian ultimatums.

-ABC News' Patrick Reevell

Some 836,000 people have fled Ukraine since Russia launched an invasion there on Feb. 24, according to the latest figures from the United Nations High Commissioner for Refugees (UNHCR).

About 453,000 of them have gone to neighboring Poland, UNHCR said.

More than 4 million refugees from Ukraine may need protection and assistance in neighboring countries in the coming months. Meanwhile, an estimated 12 million people in Ukraine are in need of emergency assistance and protection, according to UNHCR.

-ABC News' Zoe Magee

Children in Ukraine "are in grave danger, especially from the threat of explosive weapons," international humanitarian group Save the Children warned Wednesday.

"Children injured in conflict zones are at even greater risk than adults due to their specific vulnerabilities and treatment needs for blast wounds," Save the Children said in a statement. "Younger children injured in blasts are particularly at risk of death compared to adults and need to be treated differently."

At least 14 children have been killed in Ukraine since Russia launched its invasion on Feb. 24, according to the United Nations.

Save the Children, which has been delivering essential humanitarian aid to children and their families in Ukraine since 2014, called for an immediate end to violence amid fears that many more lives are at risk as Russia's military operation intensifies in major cities and satellite images purportedly show a miles-long convoy of Russian forces closing in on the Ukrainian capital, Kyiv.

U.S. Vice President Kamala Harris stopped short of calling for Russian President Vladimir Putin's ouster on Wednesday while urging for an end to the invasion of Ukraine.

"What we want is that the Ukrainian people will be free and that they will be safe. But we are now at a place where obviously Russia has yet again invaded Ukraine and we must stand in solidarity with our allies and make sure there are severe and swift consequences which is what we've been doing," Harris told ABC News' George Stephanopoulos in an interview on "Good Morning America".

When asked whether there is anything more the United States and its allies could be doing, Harris argued that the actions taken thus far have already had an effect.

"We are seeing the impact of the work that we have done. We are seeing the ruble in a free fall. We are seeing the stock market in Russia has essentially closed. What we have seen is that the credit rating of Russia is now junk," she said. "So, what we know is that we're having an impact and we're taking it quite seriously."

When pressed again that Putin appears to be willing to take the cost and is not backing down, Harris insisted: "We're going to do everything that we can to support the Ukrainian people."

"We are doing that through our security assistance, through economic assistance, humanitarian assistance," she added. "We're not going to let up."

Harris dodged a question about whether about whether U.S. intelligence now suggests that Ukraine's capital, Kyiv, will fall to Russian forces.

"This is Putin's war, and we are very concerned and we are monitoring it," she said. "We are fully aware that if there's any intentional targeting of civilians, that we are looking at the fact that there may be a violation, very well may be a violation of international law. So this is an issue that we should all be paying attention to. It is atrocious and it is a violation of all of the standards and principles that we as particularly NATO nations take seriously."

-ABC News Sarah Kolinovsky and Kelly McCarthy