In Florida, Mississippi and Louisiana, where more than 99% of the vote was counted, Kerry was leading with more than 69% of the vote. In Texas, where only 75% of the vote was counted, he held 66% in the Democratic vote.
Party delegates from those four states will bring him within easy striking distance of the 2 162 delegates he needs to formally win the nomination.
The remaining delegates are expected to come in votes in Kansas and Illinois over the next week.
With the withdrawal of his last serious rival after the March 2 "Super Tuesday" contests, Kerry is all but assured nomination at the opposition Democrats' national convention in July in Boston, Massachusetts.
He has won all but three of the more than 30 state party votes since January.
The other most serious Democratic candidates - John Edwards and Howard Dean - have dropped out of the race and were to meet with Kerry later this week to discuss common party strategy, Cable News Network reported. The Democratic race was notably lacking in the party's traditional acrimonious debate. Instead, the candidates have focussed their fire on US President George Bush, the failing economy and questions about the Iraq war.
At his victory speech in Chicago, the site of the important Illinois primary next Tuesday, Kerry challenged Bush to a debate a month from now until November.
Bush, who has no challengers for the Republican nomination, Tuesday night sewed up the number of delegates he will need for the his own party convention in New York City in late August.
Nearly eight months before the November 2 general election, Kerry holds a 48% to 44% lead over Bush, according to a national poll of likely voters by ABC Television and the Washington Post. – Sapa-DPA.
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