Mr Bildt, left, said the next round of talks would be held on 20 October
The US and EU have agreed with Bosnian politicians from all sides on new talks about constitutional reforms to break a political deadlock in the country.
The agreement came after a meeting of seven Bosnian leaders chaired by senior US and EU officials in Sarajevo.
The aim of the talks is to move the country towards eventual membership of the EU and Nato.
Bosnia struggles with an unwieldy government and deep political divisions have remained since its 1992-1995 war.
The meeting was held after the US and the EU intervened to break what is being called the worst political crisis since the war, says Mark Lowen, the BBC's Balkans correspondent.
Efforts are under way to reform Bosnia's constitution, to transfer more powers to central institutions and cut the country's vast bureaucracy, our correspondent says.
The 1995 Dayton peace accords that ended the war created a federal state with two highly autonomous entities: the Serb-dominated Republika Srpska and the Bosniak-Croat Federation of Bosnia-Hercegovina.
Friday's talks were chaired by US Deputy Secretary of State Jim Steinberg and Swedish Foreign Minister Carl Bildt, who was representing the EU.
They met Bosnian leaders including Bosnian Serb Prime Minister Milorad Dodik and Bosniak (Bosnian Muslim) officials Haris Silajdzic and Sulejman Tihic.
"We laid the basis as roughly as we expected," said Mr Bildt after the talks. He said there would be "continued deliberation inside the political parties, between the political parties and between them and us in the days to come".
He added that EU Enlargement Commissioner Olli Rehn, who was at Friday's meeting, would attend the next round of talks in Sarajevo scheduled for 20 October.
Mr Dodik warned that Bosnia-Hercegovina's constitution "should not be changed".
At present, Bosnia-Hercegovina has an unwieldy government, comprising three presidents, 13 prime ministers and 180 ministers.
Also on the table were long-standing proposals to close the Office of the High Representative - the international body that oversees all politicians in the country.
But the aim of eventual EU and Nato membership could be a long, uphill struggle, our correspondent says.
Lingering hostility between each ethnic group has led to a steady increase in nationalist rhetoric, with Bosnian Serb leader Milorad Dodik repeatedly threatening to call a referendum on secession.
That, say some Bosniak politicians, could lead to a new outbreak of violence.