MIAMI — Senators Marco Rubio of Florida and John McCain of Arizona brushed off primary challenges on Tuesday from Republican contenders.

Mr. Rubio will face a general-election race against Representative Patrick Murphy, a two-term Democrat, in a crucial contest for control of the Senate. Mr. McCain, seeking a sixth term, could also face a serious challenge, from Representative Ann Kirkpatrick, who has made it a point of her campaign to court Latinos and American Indians in an increasingly diverse and competitive state.

The contest between Mr. Rubio and Mr. Murphy is likely to be among the most expensive Senate contests in the country. With his onetime rival Donald J. Trump at the top of the Republican presidential ticket, Mr. Rubio, 45, will seek to fend off Mr. Murphy, 33, who has faced recent accusations of résumé padding.