Reuters. President Donald Trump a day earlier told the Davos forum that the leaders of Russia and Ukraine would be "stupid" if they failed to come together and get a deal done.
Witkoff said he was headed to Moscow later in the day.
Rutte expressed confidence that Trump was committed to Ukrainian independence and sovereignty.
He also said that he and U.S. President Trump had discussed in Davos how the transatlantic alliance should best defend the Arctic against Russia and China.
Trump has repeatedly said he wanted to acquire Greenland, citing national security, though on Wednesday he ruled out using force and suggested a deal was in sight to end the dispute over the Danish overseas territory following talks with Rutte.
Trump's ambitions have put strain on the NATO alliance.
Rutte said he had a "very good discussion" with Trump on how NATO allies can work collectively to ensure Arctic security, including not just Greenland but the seven NATO nations with land in the Arctic.