Officials are "hoping to get to a position where, in the near term, we have, with a lack of a better term, security guarantees" that address Ukraine's fears of another invasion by Russia in the future, Keith Kellogg said in Kyiv on Monday.
"That's a work in progress," Kellogg said of the potential security guarantees after attending Ukraine's annual National Prayer Breakfast along with politicians, business leaders and diplomats.
A week ago, Trump said he had set in motion arrangements for direct peace talks between Russian President Vladimir Putin and Zelenskiy. But Russian officials have signaled that such a summit won't happen any time soon.
Trump on Friday said he expects to decide on next steps in two weeks if direct talks aren't scheduled.
A stream of high-ranking visitors to Kyiv in recent days reflects concerns around the US-led peace drive.
Canadian Prime Minister Mark Carney visited Kyiv on Sunday for meetings with Zelenskiy, pledging two billion Canadian dollars in aid, and NATO Secretary General Mark Rutte was in the Ukrainian capital on Friday. Germany's vice chancellor and finance minister, Lars Klingbeil, arrived in Kyiv on Monday to discuss "how Germany can best support Ukraine in a possible peace process".
Putin spoke on the phone with Iranian President Masoud Pezeshkian on Monday, the Kremlin said. Russia and Iran have close relations, and Putin has also deepened ties with China, India and North Korea as Western countries have sided with Ukraine in the war.
Putin and Pezeshkian are expected to meet next week when China hosts the Shanghai Cooperation Organisation's annual summit, in Tianjin.
Klingbeil, the German vice chancellor, told Zelenskiy that Ukraine's allies have to "talk about what happens if President Putin does not relent, if he wants to continue the war."
Germany will continue to stand by Ukraine, he said, echoing sentiments by Norwegian Prime Minister Jonas Gahr Store earlier in the day.
Norway's multibillion-dollar military and civilian support for Ukraine's fight to defeat Russia's invasion will stretch into next year, Store said in Kyiv. He said he will propose to the Norwegian Parliament spending $US8.45 billion ($A13.04 billion) on Ukraine next year.
Store, whose country borders Russia, told a news conference with Zelenskiy that Ukraine is "defending a critical principle on the European level" by refusing to accept Russia's seizure of territory.
Analysts say Putin thinks he can outlast Western governments' commitment to Ukraine and use his bigger army to capture more Ukrainian land while peace efforts are under discussion.
Norway on Sunday pledged about seven billion kroner ($A1.1 billion) toward air defence systems for Ukraine. Norway and Germany are jointly funding two US-made Patriot anti-missile systems, including missiles, with Norway also helping procure air defence radar, Store said.
Ukraine's Air Force said Russia launched 104 strike and decoy drones overnight, targeting the country's north and east. There were no immediate reports of damage or casualties.
Ukraine has continued long-range drone attacks on Russia, hitting oil refineries, armouries and transport hubs and causing commercial flight disruption during the summer vacation period.
On Sunday, an Egyptian plane carrying Russian tourists from Sharm El Sheikh to St. Petersburg diverted to Tallinn because the Russian city's international airport had temporarily closed due to a drone attack, the Estonian daily Postimees reported.
Meanwhile, the Russian Defence Ministry reported intercepting 23 Ukrainian drones overnight and Monday morning over seven Russian regions, both on or near the border with Ukraine and deeper inside Russia.
