Speaking at a news conference in China, the Russian leader also said the "military hysteria" whipped up between Washington and Pyongyang "could cause a global catastrophe."
The State Department declaration requires closures in San Francisco, New York and Washington, D.C., in retaliation for a Kremlin order expelling 755 U.S. diplomatic staff. The deadline is Saturday.
The Islamic State has claimed responsibility for the attack, but Russian officials appear to discount the possibility, saying the initial investigation is not focusing on terrorism as a "main theory."
For all the talk about President Trump and Russia, he has yet to lay out a grand plan on dealing with Moscow. The Russia probes are an obstacle to cooperation. And he has resisted confrontation.
Prime Minister Dmitry Medvedev said the U.S. sanctions package "ends hopes for improving our relations with the new administration." President Trump signed the bill but called it "seriously flawed."
Congress overwhelmingly approved the legislation, but the White House has many qualms with it. Moscow has already responded to the sanctions, which also affect Iran and North Korea.
Authorities say the defendants attacked guards and managed to take their guns while being transported in an elevator. Two other alleged gang members are said to be injured and in custody.
"Trump voters are never going to fall for this collusion story and are never going to buy into this notion that the Russians rigged it with Trump," said talk radio host Rush Limbaugh this week.