"I'm no longer interested in negotiations," the US president said.
Trump explained that he has already spoken with Putin several times, but even after these talks, Russia continues to attack Ukraine.
Kremlin press secretary Dmitry Peskov, speaking to reporters on Monday, did not rule out the possibility that a meeting between Putin and Trump could take place in China in September.
Putin will visit China in early September to participate in celebrations marking the 80th anniversary of the end of World War II.
"No significant preparations are taking place for the [Putin-Trump] meeting, as there are no coordinated contacts," the press secretary said in response to a journalist's question about a possible meeting between the Russian and US leaders.
"If it happens that the US president ultimately decides to visit China on the same dates, then, of course, theoretically such a meeting cannot be ruled out if the heads of state end up in the same city," Peskov added.
Trump and Putin have spoken on the phone several times this year, but have not yet met.
Late last week, Turkish President Recep Tayyip Erdogan announced that he planned to make efforts to organize a meeting between the leaders of Russia and the United States in Istanbul to discuss a settlement to the war in Ukraine.