The Athens General Index opened down about 4%, before recovering to be 1.4% lower. On Monday, the share index had dropped 16% on the first day of trading after a five-week shutdown.
Major banks were close to the maximum 30% declines they are allowed in one day, a limit that was hit on Monday.
Banks account for about 20% of the Athens index.
Falling bank shares were offset by gains in some non-financial shares. Among the shares rising were the gaming group OPAP and some tourism-related shares such as Aegean Airlines.
The main share index is down more than 50% from last year's peak.
During the height of the Greek debt crisis, the stock exchange was closed for five weeks as part of the programme of capital controls to prevent people taking euros out of the country.
Greek investors are still not allowed to use money in their bank accounts to trade on the stock exchange.

The Australian navy ship HMAS Maitland and four merchant vessels were involved in rescue operations 75km (45 miles) south-west of Indonesia's Java Island.
The search followed a distress call on Wednesday from a vessel which said it had 150 people on board.
Indonesian teams had searched the waters, but could not locate the boat.
The country's search and rescue agency, Basarnas, sent two boats and a helicopter to the area on Wednesday but found nothing and returned to base.
But on Thursday a merchant vessel said it had found six people in the water, and more survivors were rescued during the day.
"Three survivors have serious injuries, but are in a stable condition. They are on board HMAS Maitland," the Australian Maritime Safety Authority (AMSA) said in a statement.
It added that merchant vessels APL Bahrain, Gwenolen, AR Carelia and Da Ging Xia were involved in the search.
Source: Australian Department of Immigration and Citizenship
Captain Manuel Nistorescu from the APL Bahrain ship told the Sydney Morning Herald newspaper that a group of Afghan men he picked up had been in the water for 24 hours.
There were also women and children on the missing boat, he added.
"They had an engine break and the water was coming, and the pump for pumping out the water was not working and the boat sinks. This is what I understand from them," he said.
The number of missing people could not be confirmed, Australia's Home Affairs Minister Jason Clare told reporters.
"We have grave fears for a lot more," he said. ''Don't underestimate how difficult this task is; don't underestimate how big the sea that we're searching is.''
Asylum seekers often target Christmas Island, off Australia's northwest coast, to get to the country. They make the journey from Indonesia in boats that are usually overloaded and poorly maintained.
In June, a boat with 200 asylum seekers sank near the island - 17 bodies were found and another 70 were feared dead after a three-day search. That was the second boat to sink in a week, reigniting the debate on asylum in parliament.
Earlier this month, lawmakers approved the re-opening of offshore processing camps for asylum seekers in Nauru and PNG.
The moves are aimed at deterring asylum seekers from making the dangerous journey to Australia by boat, amid an increasing number of arrivals.
Australia says it will also increase its intake of refugees to 20,000 a year, from the current 13,750, in line with recommendations by an expert panel.
Greek bank shares have fallen sharply for a second day in Athens, but non-financial firms have fared better.
[NEXT_CONCEPT]
Australian and commercial ships plucked 55 people from the sea as a search continued after a boat carrying asylum seekers was believed to have sunk.