The lawsuit filed in Delaware Chancery Court says that Al-Jazeera, owned by Qatar's royal family, failed to honor the contract in the sale of his cable channel, Current TV.
"Al Jazeera America wants to give itself a discount on the purchase price that was agreed to nearly two years ago," Gore's lawyer David Boies said in a statement.
"We are asking the court to order Al-Jazeera America to stop wrongfully withholding the escrow funds that belong to Current's former shareholders."
In the case summary from court documents, Gore and Hyatt allege fraud and breach of contract.
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"Rather than return the USD 65 million remaining in the escrow, as it was obligated to do, defendant, on June 27, 2014, submitted five claim certificates through which it attempts to manufacture several ways to retain all of the escrow balance for itself in express violation of the merger agreement," said the summary.
Al-Jazeera America, which launched its news channel a year ago, did not immediately respond to an AFP query on the suit.