WASHINGTON—Don Blankenship, the former coal magnate who served a year in prison for a mine-safety conviction, said Monday that he planned to continue his bid for a U.S. Senate seat, now as a third-party candidate after losing the Republican primary in West Virginia earlier this month.

Mr. Blankenship’s decision to remain in the race—as a candidate for the Constitution Party—follows his vow days after the May 8 primary that “it’s not over.” In addition to giving him a second shot at facing Democratic Sen. Joe Manchin in November, it enables him to extend his feud with Senate Majority Leader Mitch McConnell, who opposed his candidacy in the GOP primary.

Mr. Blankenship’s third-party hopes are complicated by West Virginia’s “sore loser” law, which was designed to prevent failed candidates of a recognized political party from refiling to run under another party’s banner.

“Now that we know that the establishment will lie and resort to anything else necessary to defeat me, we are better prepared than before,” Mr. Blankenship said Monday, adding he planned to challenge the “sore loser” law in court.