The billionaire co-founder of LinkedIn, Reid Hoffman, has pledged to give up to $5 million to veterans groups if Donald J. Trump agrees to release his tax returns before the Oct. 19 presidential debate.

Mr. Hoffman announced his challenge in a statement published Monday on Medium that said he was offering a matching donation to support a crowdfunding campaign started by Peter Kiernan, a former Marine.

By midday Tuesday, Mr. Kiernan’s fund-raising on Crowdpac.com had raised more than $74,000 toward its $1 million goal of donating funds to 10 nonprofit organizations that help war veterans. Mr. Hoffman offered to match those donations 5 to 1 up to $5 million.

He said that offer was inspired by Mr. Trump’s own pledge in 2012 to donate that amount to a charity if President Obama revealed his college and passport records and applications. At the time, Mr. Trump had been questioning whether Mr. Obama was born in the United States (indeed he was, in Hawaii).