"There are significant results," he said, after reviewing the results of Sunday's key discussions in Geneva, "and there is still much work to be done."
But from the Russians, apart from some discontented mutterings about European involvement and unauthorised leaks, the response has been somewhat muted.
Kremlin aide Yuri Ushakov said on Wednesday that Moscow viewed some elements of the latest draft positively but "many require special discussions among experts".
Separately, President Vladimir Putin's spokesman, Dmitry Peskov, said it was "premature" to think that a deal was close.
Last Wednesday already seems like aeons ago. That is when a leaked draft of a 28-point US plan to end the war first emerged.
The plan, whose references to Ukraine giving up territory and limiting the size of its military led some to describe it as a "Russian wish list", caused consternation in Kyiv and sent European diplomats scrambling to limit the perceived damage.
In some ways, it felt like a re-run of events in August, when anxious European leaders rushed to Washington to bend Trump's ear after the American president rolled out the red carpet to Putin in Alaska.
By the weekend, the Europeans had drafted a counter-proposal, also 28 points long, which replaced the blunt territorial concessions of the US plan with "negotiations on territorial swaps" and stiffened the language on security guarantees, a key concern of Kyiv.
But how much influence the Europeans had over Sunday's talks in Geneva remains unclear.
A joint US-Ukrainian statement, issued after the talks wrapped up, spoke of "highly productive" discussions, saying any future agreement must deliver a "sustainable and just peace".
Sir Keir Starmer was one of several European leaders who seized on the words "sustainable and just" as indicating that progress had been made.
Ukrainian officials sounded relieved too. The First Deputy Foreign Minister, Sergiy Kyslytsya, said the latest version of the plan had been slimmed down to just 19 points, with the most contentious issues - territory and Ukraine's future relations with Nato - put off for Trump and Zelensky to decide.
Amid recriminations over how the original 28-point version had been leaked (with fingers pointing in multiple directions), a tight veil of secrecy has been drawn around the latest version.
Despite talks in Abu Dhabi involving the US army secretary, Dan Driscoll (a new addition to Trump's Ukraine team), Ukraine's military intelligence chief, Kyrylo Budanov, and Russian officials, Ushakov says the plan has still not been discussed in detail.
With Trump's envoy Steve Witkoff due in Moscow next week and talk of Zelensky paying another visit to the White House, it seems the pace of diplomacy is not about to let up.