Mr. Trump also brushed off past declarations by his own commanders that Russia had been providing weapons and cash to the Taliban for years, but the commanders did not specifically cite any bounty program.
He later told reporters during a trip to Florida that the intelligence was “another Russia hoax.”
“They’ve been giving me the Russia hoax — Shifty Schiff, all these characters — from the day I got here,” he said, using his nickname for Representative Adam B. Schiff of California, the top Democrat on the House Intelligence Committee.
Mr. Schiff complained on Friday that U.S. intelligence officials had so far failed to provide more detailed information about the suspected Russian payments, as lawmakers were promised in early July. “We have yet to receive this information,” Mr. Schiff said in a statement.
The bounties operation is overseen by a Russian military intelligence unit, U.S. officials said. An obvious channel the Americans could use to address the issue is an important one between the top military officers in both nations, said Andrew S. Weiss, a former American official and Russia expert at the Carnegie Endowment for International Peace. But it is not known if the current officers, Gen. Mark A. Milley, the chairman of the Joint Chiefs of Staff, and Gen. Valery V. Gerasimov, the chief of the Russian general staff, have spoken of the bounties via that channel.
“Delivering a very clear and credible message that we will use all means to protect our people is the only thing that gets the Russians’ attention,” Mr. Weiss said. “Sadly, neither Pompeo nor Trump are credible messengers in that department.”
Mr. Trump and Mr. Putin have spoken eight times this year, according to a Kremlin list of the Russian president’s diplomatic activity — twice as many times as they spoke in all of 2019.
Soon after The Times first reported the intelligence assessments about the suspected Russian bounties on June 26, the State Department prepared a series of talking points warning Moscow against making payments to Taliban-linked groups in Afghanistan to kill American soldiers there, according to a U.S. official, who spoke on the condition of anonymity to discuss internal administration deliberations on the matter.