Primary election results posted by the Houston Chronicle showed that with 61 percent of the state's precincts reporting, no GOP candidate had the 50 percent needed to clinch the nomination. Dewhurst led with 46 percent to Cruz's 33 percent. Former Dallas Mayor Tom Leppert was in third place with 13 percent.
The Wall Street Journal reported Cruz -- a former state solicitor general with the backing of former Alaska Gov. Sarah Palin and other Tea Party leaders -- will face Dewhurst, who has the support of Gov. Rick Perry, in a July 31 runoff.
The Dallas Morning News reported Leppert declined to say whether he would endorse either of the two men who finished ahead of him.
On the Democratic side, Paul Sadler, with 36 percent, was expected to be in a runoff against either Grady Yarbrough, who had 26 percent, or Addie Allen, who was at 23 percent.
With Texas being a Republican stronghold, the eventual Democratic nominee will be a decided underdog in the general election.
Hutchison decided not to seek re-election after her unsuccessful run for governor in 2010.
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