“Markets are making nervous movements amid uncertainty over the global economic outlook,” said Mr Abe.
His comments put pressure on the Bank of Japan to act on a pledge it made last week to support markets.
Having fallen 5% on “Black Monday”, Japan’s benchmark index, the Nikkei 225, recovered 1% after the statement.
It had started the trading session more than 3% down but bounced back following Mr Abe’s comments.
Asian shares, along with the world’s major stock markets, were battered on Monday in reaction to the threat of an oil price war between Russia and Saudi Arabia.
Markets are already on edge from the economic fallout from the coronavirus outbreak which continues to spread globally.
“There’s uncertainty on when the coronavirus will be contained, and markets are making very unstable moves,” Bank of Japan (BOJ) governor Haruhiko Kuroda told parliament on Tuesday.
In Hong Kong, the main Hang Seng market moved up 1.7% buoyed by Japan’s moves to calm investors. The index had fallen more than 4% on Monday.
Stock markets across the world saw dramatic falls, with London’s FTSE 100 index down almost 8%.
The market meltdown was sparked by a fallout between major oil exporters Russia and Saudi Arabia who are locked in a dispute over output levels.
Russia shocked oil markets by leaving a pact with oil-exporting group Opec, leading to a 30% plunge down to around $31 a barrel.
Flexing its muscles, Russia’s finance ministry said the country could withstand low oil prices for as long as a decade.
The sharp drop in oil prices unsettled investors already reeling from a global economic slowdown caused by quarantine measures to fight the spread of the coronavirus.
Major central banks have pledged to pump cash into the financial system while governments are mulling stimulus measures to tackle the economic hit. These include cuts to interest rates to encourage companies to borrow money and expand.
However, former Bank of England governor Mervyn King told the BBC: “I don’t think that a cut in interest rates now is actually going to do a great deal to help the situation, it maybe a sign of reassurance but it is not more than that.
“What is needed now are targeted measures to help business deal with a short-term crisis and collapse of their cash flow, and I think the Bank of England understands that very well.”
Reflecting jittery markets, gold prices crossed $1,700 per ounce on Monday, the highest since December 2012. Gold is often seen as a safe-haven asset in times of economic and political uncertainty along with government bonds.