Speaking in London on Thursday, Iryna Venediktova said that between 100 and 200 new cases were coming in each day, according to the British public broadcaster.
Venediktova visited London to meet with British officials and discuss what more the United Kingdom and other Western powers could do to support the investigation process, the BBC said.
"Today we have near 14,000 cases, only about war crimes, and near 6,000 cases which are connected," Venediktova said, as quoted on the bbc.com website.
"It means that we have huge number of precedents and every day we have more and more: it's [an] extra 100, [an] extra 200, it depends on the day," she added.
She told the BBC that the most common alleged war crime was the shelling of civilian buildings, especially hospitals and schools.
In all, more than 1,000 medical and educational buildings have been destroyed, she said.
She also said that civilians were being killed in her country, and there was looting and raping.
Venediktova also revealed she had begun investigating allegations of genocide, the BBC reported.
The European Union, the United States and Britain have set up a joint group of experts to help document and analyze evidence of war crimes and other atrocities committed in Ukraine during Russia's invasion, according to an announcement.
The US Department of State said in a statement this week that the United States, the EU and the United Kingdom had created a joint initiative called the Atrocity Crimes Advisory Group (ACA).
"This joint initiative will directly support the efforts of the War Crimes Units of the Office of the Prosecutor General of Ukraine (OPG) to document, preserve, and analyze evidence of war crimes and other atrocities committed in Ukraine, with a view toward criminal prosecutions," the statement said.
The transatlantic initiative comes after the United Nations Human Rights Council this month voted to set up an investigation into possible war crimes by Russian troops in Ukraine.
Members on May 12 passed a resolution by an overwhelming majority to order an inquiry into events in Ukraine's Kyiv region and other areas that were temporarily held by Russian troops earlier this year.
The UN High Commissioner for Human Rights, Michelle Bachelet, was quoted as saying at the time that there were many examples of possible Russian war crimes in Ukraine.
"The scale of unlawful killings, including indicia of summary executions in areas to the north of Kyiv, is shocking," Bachelet said, as quoted by the Reuters news agency.
Meanwhile, Ukrainian Deputy Foreign Minister Emine Dzhaparova told the UN Human Rights Council that areas that were under Russian occupation in late February and March "experienced the most gruesome human rights violations on the European continent in decades," according to Reuters.
A Polish deputy justice minister told an international conference in Lithuania earlier this month that Poland had collected more than 1,000 witness statements on Russian atrocities in Ukraine.
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Source: PAP, bbc.com