Instability in Europe was the main factor that pushed the central bank to cut interest rates earlier this month - but it was a close call and there is no indication another cut may follow in July.
The Reserve Bank of Australia (RBA) decided to cut its cash rate by 0.25 percentage points at its June 5 board meeting.
The cut took the cash rate to 3.5 per cent, and followed a 0.5 percentage point cut on May 1.
The minutes of the RBA's June board meeting, published on Tuesday, showed the fallout from the euro area's debt problems took centre stage in the decision-making process.
"There was clear evidence of a softening in global economic conditions, and uncertainty about the future in Europe had increased significantly," the RBA minutes said.
JP Morgan chief economist Stephen Walters said the minutes revealed a close call in the rate decision.
"It seems ... that officials came close to not cutting the cash rate at all," he said.
"The domestic economy was tracking pretty much as officials had expected two weeks ago, and officials indicated that it was too early to judge the impact of the 50 basis point rate cut in May.
"Both of these points argued in favour of unchanged policy - as we suspected, though, board members were convinced to provide additional modest policy support by the weakness offshore, particularly the adverse developments in Europe."
Easy Forex currency dealer Tony Darvall said the minutes were encouraging because they showed that the June rate cut was a precautionary move due to the European situation.
"They didn't give much of an indication that the RBA would continue to cut, more that they would wait and see," Mr Darvall said.
"It also said our credit markets are not showing any sign of dislocation.
"It was all relatively better than expected."
HSBC chief economist Paul Bloxham said the RBA continued to view the domestic economy with optimism, justified by data that was released after its June rate cut.
"There's a new idea in the minutes that wasn't in the (accompanying June 5 rates) statement - that the decision was finely balanced," he said.
"This is interesting because after the decision we saw very strong GDP (gross domestic product) data and very strong employment growth."
GDP grew by 1.3 per cent in the March quarter, while unemployment remained low at 5.1 per cent in May, with 38,900 more jobs added in the month.
Mr Bloxham said conditions in the rest of the world would continue to guide the RBA's position.