By Caitlin Ostroff

Long-term Treasury yields fell Friday to their lowest levels since lockdowns started loosening, as investors sought safe assets amid rising coronavirus cases.

The yield on the 30-year Treasury fell to 1.284%, its lowest since May 1, and the yield on the 10-year Treasury hit 0.600%, its lowest since April 24. The spread between the two is the narrowest since May 15, at 0.682 percentage points, according to Tradeweb. Bond prices rise when yields fall.

The yield on the five-year Treasury briefly hit a record low earlier, touching 0.258%, according to Tradeweb.

A narrowing gap between shorter- and longer- dated bonds indicates that investors expect interest rates to remain subdued. The gap between the two had widened when investors were more optimistic about the economy emerging from the coronavirus lockdowns.

Investors are monitoring rising coronavirus cases and the likelihood of further lockdowns curtailing the recent economic recovery. New coronavirus cases in the U.S. rose by more than 63,000 Thursday, another single-day record, as hospitals in Texas, California and other states strained to accommodate a surge of new patients.

"You have increased uncertainty globally, and you have more savings, so investors are looking to put money to work in a more conservative way," said Andrey Kuznetsov, senior credit portfolio manager at Federated Hermes. "As a result this drives demand" for bonds, he said.

Bond yields have edged lower even as governments have issued more debt to fund relief efforts to combat the economic impacts of coronavirus. In the U.K., the yield on the five-year gilt, as British government bonds are known, hit a record low Thursday of minus 0.08%. Investors there anticipate that the Bank of England will implement negative policy rates in the future.

Despite continued demand for safe assets, volatility in U.S. bond markets has fallen to levels near those seen before the coronavirus pandemic. Bank of America's MOVE Index, a measure of Treasury yield volatility implied by options prices, fell to 50 on Friday after having surpassed 150 at the height of the March selloff.

This is in large part due to measures taken by the Federal Reserve and other central banks to backstop credit and funding markets, Mr. Kuznetsov said.

In stock markets, by contrast, a popular measure of future volatility known as the Cboe Volatility Index, or the VIX, has remained elevated. Stock-market investors worry that markets could return to their dramatic swings from earlier in the year. Further lockdowns to stem the spread of coronavirus could rattle fragile investor confidence, driving demand for safer assets, analysts and investors said.

Write to Caitlin Ostroff at caitlin.ostroff@wsj.com