(CNN) Mitt Romney recorded robocalls for both Sen. Marco Rubio and Gov. John Kasich's presidential campaigns in states that are voting on Tuesday, CNN has confirmed.

It's part of an escalating effort by Romney to block Donald Trump from securing the Republican presidential nomination.

The calls recorded on behalf of Rubio, which were first reported by The New York Times on Monday night , are going out in all four states voting Tuesday. On Tuesday, Kasich's campaign spokesman Chris Schrimpf told CNN the former Massachusetts governor also recorded calls in Michigan on behalf of the Ohio governor.

Romney's message may prove more effective in the crop of states voting Tuesday -- most notably Michigan and Idaho -- than it might be to the broader GOP electorate.

Romney's dad, George Romney, was the former Michigan governor, and many voters in the Mitten State still hold on to some affection for the Romney family.

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