In Europe, the FTSE 100 index of leading British shares was up 36.38 points, or 0.6 percent, at 5,760.03 while Germany's DAX rose 44.44 points, or 0.7 percent, at 6,303.97. The CAC-40 in France was 42.19 points, or 1.1 percent, higher at 3,993.49.
Wall Street was also poised to open modestly higher — Dow futures were up 16 points, or 0.1 percent, at 11,158 while the broader Standard & Poor's 500 futures rose 1.7 point, or 0.1 percent, at 1,214.
Though investors think that Greece can ride out its debt storm over the coming months after last Friday's formal request to tap the euro45 billion ($60 billion) package from the euro zone and the IMF, there are fears that the debt-laden country will need more money before an eventual restructuring of its borrowing burden.
Those worries are evident in the continuing increase in the country's cost of borrowing in the bond markets — notably the yield on Greece's two-year bonds rose to a massive 11 percent, while the spread between Greek ten-year and benchmark German equivalent spiked to an unsustainable 6 percentage points.
Greek shares languished as investors continued to fret about the country's economic prospects — there are mounting expectations that the cost of the bailout will lead to even more austerity in the country. By early afternoon Athens time, the benchmark ASE composite index was trading 2.8 percent lower at 1,805.38.
Greece does not have the money yet — Germany is still preparing to pass legislation to free up its share of the bailout package. A spokeswoman for the German Finance Ministry said Monday that minister Wolfgang Schaeuble and leading lawmakers from all parties will meet to discuss how to proceed with the necessary legislation.
"The Greek debt crisis shows little sign of early resolution and the risk is that Greece might not be able to avoid eventual debt restructuring," said Neil Mackinnon, global macro strategist at VTB Capital.
"The costs of fiscal adjustment are too high and contagion is spreading to other euro zone economies," he added.
Greece's debt crisis dominated the weekend meetings of the IMF and World Bank in Washington D.C. as well as the meeting of finance ministers from the Group of 20 major industrialized and developing economies.
The IMF's managing director Dominique Strauss-Kahn said discussions with the Greek authorities have "accelerated" and expressed his confidence that a deal will be hammered out before the next batch of Greece's debt repayments.
While stocks have managed to push higher Monday, the euro was back under pressure after gaining some respite by Greece's request for the aid last Friday — by late morning London time, the euro was down 0.3 percent at $1.33.
"With murmurs of a Greek restructuring starting to become audible and official concerns about contagion evident, it seems reasonable to suppose that investors will look increasingly cautiously at the eurozone and the euro," said Simon Derrick, senior currency strategist at Bank of New York Mellon.
While Greece's debt crisis continues to dominate headlines, there is a lot of economic news this week that could have a marked impact on investor sentiment.
Most important will likely be Wednesday's rate-setting meeting of the US Federal Reserve and Friday's first estimate of US economic growth for the first quarter of the year.
Earlier in Asia, Japan's main benchmark gained 251.33 points, or 2.3 percent, to 11,165.79, with Toyota and Honda up around 3 percent.
Elsewhere, Hong Kong's market rose 1.6 percent to 21,587.06 and South Korea's market gained 0.9 percent to 1,752.20.
Markets in Taiwan and Singapore also rose. In China, Shanghai's main stock measure lost 0.5 percent.
Oil prices fell modestly, with the benchmark contract falling 29 cents to $84.83 a barrel.
