In a post on X, Kushner wrote on Friday that Ukraine and Russia had agreed to widen the next round of negotiations to include European countries.
He said this would make it possible "to address the broader postwar European security arrangements alongside the territorial issues" between Kyiv and Moscow.
He added that Washington was working on "the largest prisoner exchange of the war."
No date or venue has been announced for the next round.
During the meeting, Putin claimed that Russia had never opposed dialogue with Europe, insisting it was the other side that had broken it off.
He warned that any plan to send Western troops to Ukraine after a peace deal would lead to a resumption of the war, because Moscow would see it as a threat to its security.
Kremlin adviser Yuri Ushakov did not confirm that Europeans would join the talks.
He said their current position on Ukraine was a recipe for endless war.
Many experts are concerned by the topics being put on the agenda, according to public broadcaster Polish Radio.
Discussing Ukraine's territory and the continent's security reflects long-standing Russian aims, they say, and Moscow wants to take territory and limit the sovereignty of European states.
Speaking at a summit of European leaders in Dublin on Thursday, Ukrainian President Volodymyr Zelensky said he found the US approach to discussing a new security order in Europe with Russia "somewhat strange."
Even so, widening the talks is seen by the EU and Ukraine as a step forward, because the Kremlin had not previously agreed to it.
Polish PM's national security adviser briefed by Trump envoys
The envoys then held talks late on Thursday at a military airport in Dublin with national security advisers.
Kushner said they came from Poland, Ukraine, Germany, Italy, France, Ireland and the EU.
Polish Prime Minister Donald Tusk said the UK was also represented and that the Americans had briefed participants on the outcome of the Moscow meeting.
Polish Radio reported that Robert Kupiecki, Tusk’s national security adviser, attended on Poland’s behalf.
Zelensky also briefly met the two American envoys.
He welcomed the news that Europeans would attend the next round, adding that he hoped the agenda would include steps towards a ceasefire and de-escalation.
Separately, Zelensky said on Thursday that the latest disruption to Starshield, the military version of SpaceX’s Starlink satellite service, was "significant" and affected the whole front line and Russian-occupied parts of Ukraine.
Similar issues were reported last month.
(ał/gs)
Source: polskieradio24.pl, Reuters, IAR