The administration had no further comment on the matter, she said.
Trump made the offer during a phone call between the two leaders, Russian presidential aide Yury Ushakov confirmed.
Although Putin and Trump met face-to-face at the G-20 summit previous year, relations appeared to remain poor amid accusations that Russian Federation meddled in the 2016 presidential election.
The prospect of Putin visiting Washington is likely to sharpen divisions in the USA over relations with Russian Federation amid continued tensions regarding alleged Kremlin meddling in the 2016 US presidential elections.
The invitation, nevertheless, seemed to represent Trump's efforts to cooperate with Putin on multiple worldwide issues.
During the March 20 call, Putin and Trump also discussed combating worldwide terrorism and the importance of coordinated efforts to limit the arms race.
Just as Mr. Trump has shown a curious reluctance to criticize Mr. Putin, even when the two countries are ejecting each other's diplomats, the Kremlin and the Russian news outlets it controls have often avoided criticizing Mr. Trump directly.
"There is certainly plenty of urgent business on the U.S. -Russia agenda, from nuclear risks to regional conflicts, but under the circumstances a lot more work still needs to be done to ensure that a summit meeting would be productive", writes Matthew Rojansky, director of the Kennan Institute at the Wilson Center, in an email to FP.
"It would be extremely important to coordinate any U.S. Russian meeting with our European allies to continue reinforcing that unity", Rojansky writes.
Mr Trump has avoided criticising Mr Putin personally and experts are anxious about the message a meeting between the pair sends in a time of increasingly strained relations between Russian Federation and the West.
There's also the issue of what might happen should the meeting actually take place. The toddler was among more than a thousand kids to roll eggs across the White House lawn. Aslund notes that Trump seems "excited" by the idea of meeting with Putin. It marked the first public event alongside his wife since 60 Minutes ran an interview with the adult film star Stormy Daniels, who says Trump paid her days before the election to remain silent about their alleged sexual encounter. "This is as awful as it can get".