U.S. Republican presidential candidate Donald Trump has criticized Democratic rival Hillary Clinton for speaking "very badly" of Russian President Vladimir Putin, remarks that follow Clinton's recent allegations that the Kremlin is trying to tilt the election in her opponent's favor.

Noting Russia's nuclear capability, Trump told a rally in Springfield, Ohio, on October 27 that Clinton is unwise to criticize the Russian leader so harshly and that Washington and Moscow would benefit from closer ties.

"She speaks very badly of Putin, and I don't think that's smart," Trump told the crowd.

He accused Clinton, who has suggested Putin considers Trump a potential Russian "puppet" in the White House, of "trying to get votes" with her stinging criticism of the Russian president.

"How do you speak so badly of somebody? I mean, how are they ever going to get along? Wouldn't it be great if we actually got along with Russia and other countries?" Trump asked, drawing cheers from the crowd of thousands.

U.S. intelligence has formally accused the Russian government of meddling in U.S. elections by directing a string of cyberattacks, including on the Democratic National Committee (DNC), ahead of the November 8 election.

Clinton has publicly accused Putin of ordering the cyberattacks in what she characterized as a Russian bid to help Trump, who has advocated repairing U.S.-Russian ties battered by disputes over the conflicts in Ukraine and Syria.

Both Trump and the Kremlin have rejected the allegations. The Republican candidate, who is trailing in most major polls, has also cast doubt on the U.S. government's charge of Russian involvement in the cyberattacks.

Trump told the crowd that it would be a "good thing" if Russia and the United States teamed up against Islamic State militants and "knocked the hell out of them."

Trump has faced widespread criticism for speaking warmly of Putin, including saying that the Russian president has been a better leader for Russia than U.S. President Barack Obama has been for the United States.

Trump's vice presidential candidate, Mike Pence, has taken a tougher line on Russia, calling Putin a "small and bullying leader" in a debate earlier this month.

With reporting by AP and Reuters

