New Zealand was the first to open and immediately went lower in the first few minutes.
Around 10.15am, the benchmark NZX-50 was down nearly 11 points to 3147 after losing 59 points on Friday.
By mid-afternoon, the NZX-50 was pointing upwards and it closed at 5pm on 3170, up nearly 12 points.
Australia's ASX-200 opened up, as did markets in Hong Kong and Japan.
Currency trading was mixed, with the euro rallying in volatile Asian trade on reports EU ministers had agreed on a 500 billion ($NZ894.8 billion) support facility for financially troubled governments.
Details were scarce because the promised statement before Asian markets opened failed to materialise.
At 4pm, the European Union delegation to New Zealand said in a statement that the council had agreed to a package of measures designed to preserve financial stability in Europe - including the 500 billion package.
"In the wake of the crisis in Greece, the situation in financial markets is fragile and there was a risk of contagion which we needed to address," it said.
The EU made a strong statement about the importance it attached to strengthening fiscal discipline and establishing a permanent crisis resolution framework.
It underlined the need to make rapid progress on financial market regulation and supervision, in particular with regard to derivative markets and the role of rating agencies.
"We need to continue to work on other initiatives, such as the stability fee, which aim at ensuring that the financial sector shall in future bear its share of burden in case of a crisis, also exploring the possibility of a global transaction tax," the statement said.
AP reported the EU's slow response to the crisis and its failure to keep Greece from getting to the brink of bankruptcy triggered slides in the euro and global stocks last week and intensified fears the crisis would spread to other countries with shaky finances such as Spain and Portugal.
Spanish Economics Minister Elena Salgado, the current president of the EU, said the ministers were determined to safeguard the currency used by 16 of the EU's 27 member states, which had come under increasing pressure since the financial meltdown of of member Greece.
BNZ senior economist Craig Ebert said while the economic implications of a deeper Greek recession were moot for the world economy, it was the broader upheaval in financial markets that was most telling.
"Push has come to shove, with Greece simply a template of what many rich-world countries face financially over the coming many years.
"In the least, we need to take the concerns around Europe's public finances and banking system seriously."
Currently, those things were disrupting the global liquidity New Zealand still heavily depended on, he said.
Foreign funding through the money markets was suddenly problematic again.
The risk premium for raising short-term money had risen.
BNZ currency strategist Mike Jones said developments in Europe would continue to provide most of the direction for the New Zealand dollar this week.
Early indications were that the rescue package had eased markets' contagion fears, he said.
