Mr Kasich did not have a path to secure the nomination outright, but pledged to lobby for his candidacy during the Republican convention in July.
Mr Trump holds a commanding lead and is closing in on the nomination.
Despite being a popular governor, Kasich only won his home state.
Texas Senator Ted Cruz dropped out of the race on Tuesday after losing to Mr Trump in the Indiana primary.
Mr Kasich cancelled events in Washington and announced an evening event in his home state on Wednesday.
Earlier on Wednesday, he released a Star-Wars themed advert describing himself as the "only hope" against Donald Trump.
Mr Kasich had been widely seen as the most moderate and electable Republican candidate and polled well against Hillary Trump, but that did not garner him enough support among Republican voters.
He promoted an optimistic message while campaigning, shunning negative attacks against other candidates.
Florida Senator Marco Rubio, who dropped out in March, garnered more delegates than him during primary elections.

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