The meeting had been announced last week and was supposed to take place in Budapest, Hungary, although a date had not been set.
The decision was made following a call between US secretary of state Marco Rubio and Russian foreign minister Sergei Lavrov.
Kremlin spokesperson Dmitry Peskov indicated on Tuesday there was no sense of urgency for Mr Trump and Mr Putin to meet, saying that “preparation is needed, serious preparation”.
The back-and-forth over Mr Trump’s plans is the latest bout of whiplash caused by his efforts to resolve a conflict that has persisted for nearly four years.
Earlier, Ukrainian President Volodymyr Zelensky and European leaders accused Mr Putin of stalling for time to continue his invasion as diplomatic efforts took place.
They also said they opposed any push to