Turkey has said it is not satisfied with the EU's reasons for not opening membership talks in the area of economic and monetary policy.
Turkey's EU membership talks lurch from one crisis to another
The talks were delayed because France signalled objections, reflecting President Nicolas Sarkozy's opposition to Turkey joining the European Union.
But membership negotiations were started in two other areas on Tuesday.
Turkey's chief negotiator, Ali Babacan, said Ankara hoped the problems would be overcome in the next six months.
"We are not satisfied with the technical justifications that were given to us and we hope that there will be progress in this matter during the Portuguese presidency," he said.
Turkey and the euro
Germany, which will hand the EU presidency over to Portugal on 1 July, had hoped to make more progress with the negotiations during its six months in charge.
Science and research
Enterprise and industry
Economic and monetary policy
Free movement of goods
Right of establishment and freedom to provide services
Agriculture and rural development
The BBC's Oana Lungescu in Brussels said France's decision to delay the talks on economic and monetary policy was intended to demonstrate that Mr Sarkozy was keeping an election promise to keep Turkey out of the EU.
A French diplomat said discussing monetary union with Turkey implied that Turkey could one day adopt the euro.
There are 35 policy chapters which must be successfully negotiated before a country can join the EU.
Turkey now has four chapters under way.
Croatia, which began membership talks at the same time as Turkey, opened six more chapters at Tuesday's talks, bringing its total to 12.
Croatia seems well on track to become the EU's 28th member by the end of the decade, our correspondent says, provided it continues reforms and tackles corruption. But Turkey's bid, she says, seems to go from crisis to crisis.
The EU suspended negotiations on eight chapters last year, after Turkey failed to open its ports and airports to traffic from EU-member Cyprus.
It has decided that chapters not linked to trade policy can still be opened, but not closed until the Cyprus issue is resolved.