The divisions have, if anything, increased the excitement and the value of all the virtual currencies in the world — and banks and governments have announced their own projects to harness the technology.

The price of Bitcoin has recently been at record highs, near $3,000, and several other coins have grown to be worth billions of dollars on their own. A whole class of companies have raised money in recent months by creating and selling their own new digital tokens.

Until now, though, Bitcoin has remained the most valuable digital token of them all, and it has kept its followers united by a single set of rules, despite all the warring behind the scenes.

The divisions, though, appear to have grown too stark to keep everyone on the same blockchain, as the ledger of all Bitcoin transactions is known.

Mr. Ver has been one of the leaders of a contingent that has long wanted to change the rules governing the Bitcoin network so that it can handle more transactions and compete with the likes of PayPal and Visa.

Bitcoin Cash is set to increase the limit on the number of transactions that can be processed by the Bitcoin network every 10 minutes. Currently, the network can process only blocks of transactions that are smaller than one megabyte, which allows for roughly five transactions in a second.

The move to increase the size of the so-called blocks, though, has run up against intense opposition from the programmers who maintain the Bitcoin software.