These investors are cautious as the last few times bitcoin has tested these levels it led to sharp sell-offs. On March 10, bitcoin fell to $1,085. Later in March, the digital currency dropped from around $1,260 to $950 over the course of a few days.
The reason for the recent climb in bitcoin prices is optimism after an announcement in the U.S. that the Securities and Exchange Commission (SEC) is reviewing its decision to reject a bitcoin exchange-traded fund (ETF) proposed by Cameron and Tyler Winklevoss.
Last month, the SEC denied an application by the Winklevoss twins to list the ETF on the Bats BZX exchange. The price rose on hopes that the application will get another shot at approval once the decision is reviewed, but disappointment could bring bitcoin prices back down.
However, others remain bullish. Pavel Matveev, co-CEO of blockchain personal finance platform Wirex, predicts the price of the cryptocurrency could reach as high as $3,000 this year.
"Bitcoin has doubled in value in the past six months. The trend for financial regulation, which recognises bitcoin, is spreading across Asia-pacific, and we expect more and more countries to regulate virtual currencies. I believe the price will continue growing and reach as much as $2,000 to $3,000 by the end of the year," he told CNBC via email.
Other factors will boost bitcoin, such as Japan's recent decision to recognize bitcoin as legal tender.
"Bitcoin does face certain challenges such as negative perceptions stemming from past instances of hacking and other illegality. The Japanese financial system will also face a steep learning curve regarding how to report bitcoins in accounts, for example," he added.
"At the same time bitcoin is rapidly integrating such challenges and is increasingly becoming more robust, as Japan's official recognition of the cryptocurrency suggests. Integration into the financial system means companies can now more easily develop products and services."
- CNBC's Arjun Kharpal contributed to this report.