A rule in the original software, released in 2009, limited the number of transactions that could move through the system to about five a second.

In the last two years, an outspoken group of Bitcoin aficionados wanted to see the currency expand quickly to compete with Visa and PayPal.

But that camp faced opposition from the so-called core developers, a few dozens programmers who maintain the basic Bitcoin software, generally on a volunteer basis.

At the end of July, some of the people who wanted Bitcoin to expand quickly broke off and created a rival digital money, known as Bitcoin Cash, that can handle more frequent transactions.

That new currency has attracted a small following, and retained a relatively stable value around $300.

Most Bitcoin investors and companies, however, have stayed with the original Bitcoin network and the core developers who are working on it.

The core developers have come up with their own solution to increase the number of transactions running through the system, known as Segregated Witness, or SegWit.

While SegWit does not expand the network as quickly as Bitcoin Cash, it makes it easier to build services on top of the Bitcoin network, such as the so-called Lightning Network, that will allow for faster transactions.

The biggest backers of the network agreed last week to proceed with SegWit, and it is that agreement, on scaling the network, that is the most obvious reason for the recent surge.

Scaling has been the major catalyst for the price rally, said Charles Hayter, the founder of the data company CryptoCompare. The scaling debate has certainly been holding the Bitcoin price back.

Many backers of the core developers have said that Bitcoin is more likely to be a base layer that other services are built atop. In this vision, Bitcoin would be more like gold in the old gold standard than like a payment network.

The gold analogy and the scarcity of Bitcoin the rules of the network dictate that only 21 million will ever be created have led some investors to believe that the value of the currency will continue to rise as more people look to store their wealth in the system.

This vision has caught particular fire in Japan and South Korea, which have accounted for an increasing proportion of all Bitcoin trading this year, taking over from China, which once was responsible for the highest trading volume.

The introduction of SegWit does not resolve all of the arguments that have divided the Bitcoin community.

Many large Bitcoin companies are still hoping to follow through with an agreement, reached in the spring, that would change the Bitcoin software in November to allow twice as many transactions to flow through the network.

The core developers have made it clear in various forums that they do not plan to update the software in November to double the network capacity. When the November deadline is reached, some of the companies hoping to double the network capacity could again split off from the core developers.

There is a history of animosity between Bitcoin factions with vested interests, and these tensions could flare up again, Mr. Hayter said.

For now, though, Bitcoin has been rising steadily, and much faster than any of the competing virtual currencies that have cropped up in recent years.

Earlier in the year, the prices of many other virtual currencies were rising faster than the price of Bitcoin, most of all Ethereum, a virtual currency that has more programmable features than Bitcoin.

The price of Ethereum has been rising this month, but more slowly than Bitcoin and it remains below the record high it reached in June. On Monday, the price stood around $300.

Investors are buying Ethereum and Bitcoin to invest in so-called initial coin offerings, a new method of fund-raising in which entrepreneurs create and sell their own virtual currencies.

Such offerings have continued to come onto the market despite warnings from regulators that some of them may violate securities laws.

A version of this article appears in print on August 15, 2017, on Page B3 of the New York edition with the headline: The Price of Bitcoin Surges After an Agreement on a Key Software Update.

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Bitcoin Price Surges After Agreement on Software Update - New York Times