WASHINGTON—Republican Rep. Chris Collins of New York said Saturday he is suspending his re-election campaign amid insider-trading allegations that have derailed what had been viewed as a clear path to another term.

“I have decided that it is in the best interests of the constituents of NY-27, the Republican Party and President Trump’s agenda for me to suspend my campaign for re-election to Congress,” Mr. Collins said in a statement on his official campaign Twitter page.

He...