Judge James Peterson said during a hearing Friday morning in Madison that there was no question that he must deny the request for an injunction.
The pro-Trump groups, the Great America PAC and the Stop Hillary PAC, filed a federal lawsuit Dec. 1, the day the recount began, seeking to stop the process.
In explaining his decision, Peterson said Trump has made claims of voter fraud and a "mandate" in elections ,"so the count matters." Peterson said nothing about the recount impugns the integrity of elections.
Trump defeated Hillary Clinton by more than 22,000 votes in the state. Green Party presidential candidate Jill Stein requested the recount to determine whether election machines were hacked.
Wisconsin's recount was more than 82 percent complete as of Wednesday. So far Clinton has gained 61 votes.
Stein is also seeking recounts in Michigan and Pennsylvania. A federal judge in Michigan has halted that state's recount. A federal judge in Pennsylvania will hold a hearing Friday on whether that recount can begin.
Copyright 2016 by Channel 3000. The Associated Press contributed to this report. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.