Describing the senator from Texas as "nice and supportive," Trump told CNBC's "Squawk Box" on Monday that the two candidates have similar ideas on many of the issues, including border security and the need for a wall to keep out illegal immigrants.
"[But] If he catches on, I guess we'll have to go to war," Trump said of Cruz, who's seen a bit of a bump nationally and in the early contest states of Iowa and New Hampshire since last week's Republican debate.
Outsiders Trump and retired neurosurgeon Ben Carson still hold a commanding lead in the race. They're neck and neck in polls nationally and those conducted in Iowa and South Carolina.
But in other primary states, Trump was ahead of Carson in New Hampshire and Florida, according to the RealClear Politics average of the latest polls.
"We're doing very well. The message is resonating," said Trump, who characterized his manner as "tough talk" but "common sense talk."