Donald Trump, the Republican US presidential front-runner, is apparently "honored" that Russian President Vladimir Putin considers the real-estate magnate a "flamboyant" and "very talented" man.

"It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond," Trump said in a statement, according to Politico.

He continued: "I have always felt that Russia and the United States should be able to work well with each other towards defeating terrorism and restoring world peace, not to mention trade and all of the other benefits derived from mutual respect."

During a separate press conference earlier in the day, Putin raised eyebrows when he reportedly said that he would welcome stronger relations under a Trump administration.

"He is a very flamboyant man, very talented, no doubt about that. ... He is an absolute leader of the presidential race, as we see it today," Putin told reporters, according to Reuters. "He says that he wants to move to another level of relations, to a deeper level of relations with Russia. How can we not welcome that? Of course we welcome it."

But at least one Republican rival was displeased with what some commentators see as a budding bromance between Putin and Trump.

US Sen. Lindsey Graham (R-South Carolina), who has trailed in the polls, sent out a series of tweets mocking Trump: