The Belgian politician leading talks to form a new government tendered his resignation on Sunday, but the king insisted he stay on to avert a political crisis two months after a parliamentary election.
French-speaking Socialist leader Elio Di Rupo, whom King Albert had asked to pave the way for a new government, said in a statement that two parties from Dutch-speaking Flanders had been unwilling to continue negotiations.
After more than three hours of talks with the Belgian monarch, the palace said that Di Rupo had sought to be discharged, but the king had rejected this demand and asked him to continue his work.
Mr Di Rupo accepted, the palace said in a statement.
Di Rupo has been seeking to balance Flemish demands to gain more powers for Flanders and the concerns of French speakers, who fear their poorer region will suffer from devolution and that the process will eventually lead to Belgium breaking up.
Di Rupo is the second adviser to be appointed by the king. The head of Flemish separatist party N-VA, which won the most seats in the June election, abandoned his mission in July, saying there was not enough agreement on key issues.
Di Rupo said N-VA and the Flemish Christian Democrats were the parties that brought negotiations to an end.
A collapse of talks would have left Belgium in political turmoil. Di Rupo is widely tipped to become prime minister. There is no obvious alternative candidate and little sign that the parties can agree a coalition deal.
Belgium, whose national debt is as large as its annual output, can ill-afford political paralysis at a time when financial speculators are on the look-out for budgetary laggards.
Caretaker Prime Minister Yves Leterme has bought some time by passing a bill to reduce the budget deficit to 4.8 percent of gross domestic product this year, from a previous plan of 5.6 percent.
However, a new government should already be setting out plans for 2011 and beyond.
Di Rupo has said he plans to hold a news conference on Monday.
(Reporting by Philip Blenkinsop; Editing by Jon Boyle)