Donald Trump should not be too proud that Vladimir Putin has called him a "bright and talented" candidate, Marco Rubio, one of the tycoon's main rivals in the race for the GOP's presidential nomination, warned over the weekend.

That's because, according to Rubio, the Russian president has "jailed and murdered journalists [and] political opponents" and is not a leader to be emulated. While Washington will need to continue to "deal with [Putin]" from a "geopolitical, realistic level," the former KGB agent "is not someone who is going to go down in history as a great leader," the Florida senator judged, according to CBS's "Face the Nation."

Attacking President Barack Obama, however, Rubio added, "[Putin is] running his country and at least he's a leader, unlike what we have in this country."

In an attempt to gain some traction in the crowded Republican field of White House hopefuls, the Cuban-born presidential candidate has come out swinging in recent days. He also ripped the GOP's other Hispanic candidate, Ted Cruz, accusing the Texas senator of flip-flopping on multiple issues, ranging from immigration to trade policies, The Hill reported.

"There are multiple issues on which (Cruz has) tried to do these sorts of things," Rubio alleged. "For example, when the free trade agreement was up he wrote an opinion piece in the Wall Street Journal, he wrote it with Paul Ryan. And just three days later he flipped on it. I don't know why. He got some pressure on the fast-track authority."

On immigration, an issue on which Cruz has tried to differentiate himself from his Senate colleague, their approaches are more similar than the Texan likes to claim, Rubio insisted.

The Foreign Relations Committee member pointed to an amendment Cruz had offered for the controversial 2013 immigration reform bill that would have prevented undocumented immigrants from gaining a path to citizenship, but would have allowed them to apply for work permits and permanent residency after 10 years.

"I think [Cruz] wanted to not talk about legalization during the primary and leave himself the option of being for it in a general election," Rubio suggested on CBS. "I don't think that's fair to the electorate."