One of the groups that is urging Republicans to dump Donald J. Trump at their convention next month will start showing a new ad that tells delegates to follow their conscience and vote for someone else.

The campaign, which will be focused mainly on Fox and Fox News and cost about $70,000, is part of an effort by anti-Trump forces to raise awareness of their efforts before the convention begins in Cleveland in less than four weeks.

They face an uphill climb. Mr. Trump is so far guaranteed more than 1,500 delegate votes, which gives him more than the majority he needs to secure the nomination. But groups like the one behind the new ad, Delegates Unbound, are arguing that under the proper interpretation of Republican Party rules, delegates are free to vote however they see fit.