MOSCOW (Reuters) - President Vladimir Putin would respond in kind if the new U.S. administration showed willingness to talk, a Kremlin spokesman said on Sunday, while also accusing Washington of meddling in mass protests in support of detained opposition leader Alexei Navalny. The Kremlin also downplayed the scale of Saturday’s demonstrations, which saw police detain more than 3,000 people and use force to break up rallies across Russia. Prior to the protests, the U.S. Embassy in Moscow had issued a “Demonstration Alert”, warning U.S. citizens to avoid the protests and naming the venues in Russian cities where protesters planned to gather. “Of course, those publications are inappropriate,” Kremlin spokesman Dmitry Peskov told Rossiya 1 TV on Sunday, according to Interfax news agency. “And of course, indirectly, they are absolute interference in out internal affairs. So, this is a direct support of the breach in the Russian Federation’s law.” The embassy, in emailed comments, said such warnings were a “common and routine practice” of many countries’ diplomatic missions. “U.S. embassies and consulates around the world regularly issue safety and security messages to our citizens,” it said. The United States on Saturday called on Russian authorities to release protesters and journalists detained at the demonstrations, and condemned what it called “harsh tactics” used by the police against them. In central Moscow, where Reuters reporters estimated up to 40,000 people had gathered in one of the biggest unauthorised rallies for years, police were seen roughly detaining people and bundling them into nearby vans. The authorities said just around 4,000 people had shown up, while the foreign ministry questioned Reuters’ crowd estimate. “No, only a few people went out, many people voted for Putin,” Peskov said, according to the TASS news agency. He added that the Russians have supported constitutional reforms proposed by the president. Changes to the constitution will allow Putin to stay in power until 2036. RELATIONS LOWEST IN YEARS Navalny had called on his supporters to protest after being arrested last weekend as he returned to Russia from Germany for the first time since being poisoned with a nerve agent he says was slipped to him by state security agents in August. Even before the friction over Navalny, relations between Moscow and Washington have been at their lowest since the end of the Cold War, with the two sides also at odds over Russia’s role in Ukraine and allegations of its meddling in U.S. elections, which it denies, among other issues. But Peskov had, nonetheless, struck a more conciliatory tone earlier on Sunday, when he said Russia was ready to set up a dialogue with the new administration of President Joe Biden. “Of course, we count on success in setting up a dialogue,” he was quoted as saying on TV by Interfax news agency. “This will be the dialogue where, of course, differences will have to be stated to a greater extent, points of differences. But at the same time, a dialogue is a possibility to find some rational kernels, the little parts where our relations are getting closer,” he said. “And if the current U.S. administration is ready for such an approach, I have no doubts that our president will respond in kind.” Putin was one of the last global leaders to congratulate Biden on his victory in the U.S. presidential election after the Nov. 3 vote. One of the burning issues to be resolved by the two nuclear powers is the arms control treaty, known as New START, which is due to expire on Feb. 5. The White House said last week that Biden would seek a five-year extension to the deal, while the Kremlin requested concrete proposals from Washington. Washington was joined by the European Union and Britain in condemning the security forces’ handling of Saturday’s protests, while the foreign minister’s of Italy and France on Sunday both expressed support for sanctions against Moscow.