By Andrey Ostroukh

MOSCOW--Russia's ruble hit fresh record lows on Tuesday, as investors grew worried the central bank might take more drastic steps, such as boosting interest rates sharply or accelerating a planned shift to a free float, as other efforts to slow the currency's slide have so far had little effect.

Russia's former finance minister Alexei Kudrin said on Tuesday that the central bank needs to let the ruble float freely earlier than the initial plan to do so in 2015, Russian news agencies reported. The Kremlin has already warned it won't burn the reserves "thoughtlessly."

"There is a rumor on the market that the central bank may let the ruble float freely. If they scrap the trading band, there might be another spike higher [in the dollar] despite a widely expected hike to interest rates," said Igor Akinshin, a dealer at Alfa Bank.

The ruble has been hitting historical lows almost daily this month, as the price of oil, one of Russia's key exports, has dropped below $90 a barrel. Meanwhile, Russian banks and companies have been stocking up on dollars and euros at home, after being cut off from borrowing abroad by Western sanctions.

Also on Tuesday, Russia's finance ministry skipped its third weekly treasury-bond auction in a row, citing unfavorable market conditions. Such cancellations are becoming increasingly familiar now that Russian borrowing costs are rising, but investors and analysts apparently aren't overly concerned.

"The key thing is that the government has some flexibility with regards to local bond auctions because the budget for this year at least is looking reasonable. It has opted to cancel these auctions rather than pay high interest rates," said Neil Shearing, chief emerging markets economist at Capital Economics.

The situation is manageable for this year, Mr. Shearing said. Next year, however, could become ugly if oil prices remain low and sanctions remain in place, he said.

The central bank has introduced currency swaps and foreign-exchange repurchase agreements to provide dollars to the market, which is hungry for foreign currencies. The finance ministry also has pledged to provide banks with dollars, but the selling pressure on the ruble has only increased. The central bank has sold over $23 billion this month to buttress the home currency, but the ruble has still dropped nearly 7% against the dollar.

The central bank and the government have ruled out capital controls as a way to save the ruble from falling, so the next steps, say economists, could be a big rate increase or a quicker move to a free float, a shift originally set for January 1. Both measures would be potentially painful, as a rate rise would hurt the stagnant economy, while a float could lead to a sharp drop in the value of the ruble.

On Tuesday, the ruble hit a record low of 42.60 versus the dollar, bringing the year-to-date depreciation to 23%. Against the euro, the Russian currency weakened to a record low of 54.19.

"The continued slide in the ruble over the past few weeks has raised the prospect that Russia is in the grip of a self-fulfilling currency crisis in which the mere anticipation of currency weakness spurs further capital outflows and pushes the ruble even lower," research firm Capital Economics said in a note on Tuesday.

The ruble's behavior this month isn't typical for the second half of the month, when export-focused companies usually convert dollar and euro revenues to meet local tax duties.

According to Gazprombank estimates, Russian companies had to pay some 650 billion rubles ($15.3 billion) in the first two days of this week but that did little to underpin the ruble. Given the ruble's steady depreciation, export-focused companies are in no rush to convert foreign currencies for tax duties.

The central bank's predictable interventions make it easier for market participants to bet on the ruble's depreciation. According its practice in interventions, the central bank starts selling $350 million if the ruble eases to the weak end of its trading corridor. Once the allotment is exhausted, it shifts the band 5 kopecks higher and starts spending reserves again.

On Tuesday, the ruble hovered at its historically weakest value of 47.77, suggesting its nine-ruble-wide band stood at 38.80-47.80 against a euro-dollar basket. Thus the central bank shifted the ruble's band 68 times so far this month and carried out the heaviest intervention since March when the central bank had to step in to save the ruble following Moscow's intention to send troops to Ukraine's region of Crimea.

The Bank of Russia, which doesn't comment on the exact timing of switching to the ruble free float, remains the last hope for those who would like to see a stronger ruble. The bank has pledged to intervene if needed even after it lets the ruble float freely and is working on ways to provide the market with hard currencies without drawing on reserves, which stood at around $450 billion last week.

On Wednesday, the central bank is set to hold its first auction of foreign-exchange repurchase agreements, in which it will offer banks $1.5 billion for four weeks. At a one-week auction on Thursday banks will be able to borrow $2 billion from the regulator.

The central bank is also widely expected to raise interest rates at its board meeting on Friday, as inflation has reached 8.3% on the year, overshooting the central bank's 2014 targeted ceiling of 6.5%.

To regain initiative the central bank needs to raise interest rates this week by more than the market expects, Capital Economics said. The research firm suggested that the market expects the central bank to raise rates by 50 basis points, though some banks, including Morgan Stanley, said recently a 100-point rate hike could be possible by the end of the month.

Expectations of a rate increase push ruble bond yields higher, increasing attractiveness of buying into Russian debt. But at the same time climbing rates make the finance ministry reluctant to raise funds by selling high-yielding Treasury bonds. On Tuesday the ministry said it canceled its weekly treasury bond auction for the third week in a row, citing unfavorable market conditions.

--Emese Bartha contributed to this article.

Write to Andrey Ostroukh at andrey.ostroukh@wsj.com