Asian shares rebounded Tuesday morning from the previous session's steep falls, but investors remained wary as Cyprus’ Parliament prepared to vote on an EU bailout.

Confidence was partially restored by news Monday that the Eurogroup decided to give Cyprus more flexibility over a tax on bank accounts that is part of the bailout conditions, after a teleconference of euro zone finance ministers, Reuters reported.

A Greek Finance Ministry source said Cyprus would still need to raise 5.8 billion euros from the levy as planned, but could exempt smaller savings accounts.

Tuesday's vote in Cyprus, originally planned for Sunday, has been postponed twice already in an effort to build consensus in a fractious parliament where no party has an absolute majority. Three parties have said outright they will not support the tax.

Banks are to remain shut on Tuesday and Wednesday to avoid a bank run

The MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.5 percent after slumping 1.5 percent to its lowest level since Jan. 2 for its steepest one-day fall in two weeks on Monday.

South Korean shares led the pack with a 1 percent jump, as bargain hunters drove the market up from Monday's one-month lows, while Australian shares added 0.1 percent, effectively maintaining Monday's 2 percent loss.

Japan's Nikkei gained back 2 percent after shedding 2.7 percent for its biggest one-day percentage drop in 10 months on Monday as the yen rose broadly. Japanese financial markets will be closed on Wednesday for a holiday. .T

Benchmark 10-year U.S. Treasury yield inched up 1 basis point to 1.967 percent in Asia while 10-year Japanese government bond yields also added 1 bps to 0.595 percent.

"The worry about Cyprus is overdone, as the scenario there is unlikely to spread to bigger euro zone countries. Global markets were due for a correction after last week's long rally," Lee Young-gon, an analyst at Hana Daetoo Securities, told Reuters.

Global stock markets fell on Monday following the euro zone's decision over the weekend on partially funding a bailout of Cyprus by taxing bank deposits, raising fears the measure could set a precedent for future euro zone bailouts, and destabilize its financial system.

U.S. and European shares fell Monday, slipping further from multi-year highs hit last week, hitting shares in southern European lenders the hardest, while Italian and Spanish bond yields jumped on Monday. Safe-haven German yields hit 2013 lows.

The euro hit a three-week low of $1.2882 on Monday but was trading at $1.2944 early on Tuesday in Asia.

Against sterling, the euro stood at 85.75 pence, near a five-week low of 85.34 pence hit on Monday. On the yen, the common currency traded at 123.47 yen, having recovered from Monday's low of 121.585 yen.

The dollar held steady around 82.725 against a basket of currencies, after inching closer on Monday to a seven-month high of 83.166 hit last week.

While investors were watching Cyprus, many doubted serious contagion from the small island state to the broader European system.

"The uncertainties and potential fallout from the bailout plan in Cyprus have brought systemic risk back to the table," Morgan Stanley said in a research note, adding the situation could add to funding stress in the near-term.

"However, we note the level of stress is significantly lower than in the first half of 2012. This, in combination with still-abundant liquidity, portfolio reallocations into the (emerging market) asset class, and normalizing growth should keep periods of systemic risk short-lived and contained in nature," it said.