Celebrating his two wins, Trump, 69, criticised the establishment Republicans who have led recent attacks on him, including heavy negative advertising.
In Mississippi, the real estate tycoon received the support of nearly 50 per cent of the Republican voters. Senator Ted Cruz came second with 35.2 per cent of the votes counted.
In Michigan, Trump received 37.2 per cent of the Republican votes. To the surprise of many Cruz was pushed to the third spot by the Ohio Governor John Kasich in the state who received 25.5 per cent of the votes. Cruz gained the support of 23.7 per cent of the votes.
She won Mississippi by 88 per cent to 10 per cent, bolstered by her overwhelming support among African American voters.
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With Mississippi win, Clinton has grabbed 21 delegates at stake taking her total count to 1,134. To win the party's presidential nomination, she needs 2,384 delegates of the total 4,765.
Before today's primaries, Trump was leading with 384 delegates. He needs least 1,237 votes from a total of 2,472 delegates.
In addition to Michigan and Mississippi, Republican presidential primaries are also being held in Hawaii and Idaho.
After registering impressive primary wins, Trump exuded confidence of easily defeating his Democratic rival Hillary Clinton in the November presidential elections.
"I am going to beat Hillary (Clinton). Hillary is going to be very very easy to beat. She is a very easy target, if she is allowed to run. If the government does its job properly, she would not allow to run," Trump told reporters at a late night news conference in Florida.
Asserting that he is a Republican unifier, he urged the party establishment to embrace his movement and the massive support that he is getting.
This he said would help the Republican party to win the presidential elections.
Trump claimed that he would win some of the States like New York where the Republican party normally does not win.
In his victory-speech-cum-press conference, the New Yorker said his rivals - Cruz, Rubio and Kasich - have not done well.
Responding to questions, he attributed his impressive wins to his distractors who are running advertisements against him and Mitt Romney, the former presidential candidate, for criticising him.