COLORADO SPRINGS — Senator Ted Cruz captured a majority of Colorado’s delegates to the Republican National Convention on Friday, outmaneuvering Donald J. Trump, whose lack of an organized national campaign once again allowed Mr. Cruz to gain at his expense.

As the fight for the Republican campaign moves into a period in which a handful of delegates could decide the nomination, Mr. Trump’s losses here were a troubling sign.

Colorado awards its delegates differently from the way most states do. Instead of holding a statewide primary — the kind of contest Mr. Trump is used to commanding through his dominating and ubiquitous media presence — it is using a series of caucuses.

Before this week, registered voters selected local delegates, who tend to be more conservative party loyalists, ones Mr. Trump has had trouble winning over. Those delegates, in turn, have been voting this week on delegates to the national convention, most of whom are pledging their support to one candidate or another.