Wall Street strategist Tom Lee told CNBC he remains bullish on bitcoin and bets on a recovery soon despite prices of the world's largest cryptocurrency falling to their lowest levels in more than year on Tuesday.

Last week, Lee cut his year-end bitcoin target to $15,000 from $25,000.

In Tuesday's CNBC interview, he stood by that forecast, which would represent about a 250 percent increase from early morning lows of around $4,200.

Prices were falling 15 percent Tuesday, bringing their seven-session slide to about 30 percent.

"Days like this, it does make me wonder" about my prediction, the Fundstrat Global Advisors co-founder said on "Squawk Box." "This past few days has definitely been a negative development."

However, Lee contended that more institutional involvement and oversight from U.S. regulators could bolster prices into the end of 2018.

Lee put "fair value" of bitcoin at $7,000. Prices would have to rise about 66 percent to get back there.

He also said the downturn in tech stocks could be hurting bitcoin investors.

— CNBC's Kate Rooney contributed to this report.