(Adds Kansas results)
By Carey Gillam
KANSAS CITY, Mo., Aug 5 (Reuters) - U.S. Republican Senator Pat Roberts appeared headed for victory in a primary election challenge on Tuesday by a Tea Party-backed physician with family ties to President Barack Obama.
With 86 percent of precincts reporting, Roberts had 48 percent of the vote and Milton Wolf 41 percent in the four-candidate field, according to the Kansas secretary of state.
Roberts has had a 47-year career in Congress and faced conservative challenger Wolf, a doctor who said he wanted to "save the Republic."
Wolf acknowledged a distant family tie to Obama but built his campaign on promises to repeal many of the Democratic president's policies. In an interview with CNN, Wolf promised "the mother of all family feuds to save America," if elected.
Also in Kansas, with 82 percent of precincts reporting, incumbent Republican Congressman Mike Pompeo had won 63 percent of the vote, and looked to be beating back challenger Todd Tiahrt in a race that had turned into a fight over food labeling.
Pompeo, backed by powerful food and agriculture companies, recently introduced legislation to nullify state efforts to require labeling on foods made from genetically modified crops.
Laws mandating such labeling are being pursued in several states, and Tiahrt has found support in colliding with Pompeo over the issue.
"Tiahrt appears to be running a 'scorched earth' policy of attacking many traditional Republican donors and supporters in an effort to paint himself as a populist," said Michael Smith, political science professor at Emporia State University.
Pompeo succeeded Tiahrt in the House of Representatives when the latter made an unsuccessful U.S. Senate bid in 2010.
The other U.S. states holding primaries are Missouri, Michigan and Washington.
Voters in Missouri will have a say on whether John "Jay" Ashcroft, whose father, John Ashcroft, was Missouri governor, U.S. attorney general and a U.S. senator, moves forward in his bid for an open seat in the state senate.
Five of Missouri's U.S. Representatives face primary challengers but are expected to hold their seats going into November's general election.
In Michigan, the Republican primary features incumbent U.S. Representative Justin Amash and challenger Brian Ellis. Amash is a Tea Party favorite and member of a rebel group of House conservatives known for their resistance to compromise, while Ellis is the head of an investment firm who bills himself as "West Michigan Nice" for his collaborative style.
Also in Michigan, U.S. Representative Kerry Bentivolio, known as a reindeer farmer and Santa Claus impersonator, looks poised to lose to challenger Dave Trott, which would make Bentivolio the third incumbent Repulican congressman to lose in a primary so far this year.
In Washington state, retired Microsoft engineer Pedro Celis is taking on businessman and perennial candidate "Mike the Mover," formerly known as Michael Shanks, to represent the 1st Congressional District.
Celis, former chairman of the Republican National Hispanic Assembly, is expected to win the primary easily to face off in November against the incumbent Democrat, U.S. Representative Suzan DelBene. (Additional reporting by Kevin Murphy in Kansas City; Editing by Eric Walsh, Doina Chiacu, Sharon Bernstein and Clarence Fernandez)