"The king and the prime minister jointly underlined that ... a political crisis would be inopportune and would seriously damage both the economic and social well-being of the citizens and the role of Belgium in Europe," the palace said in a written statement.
Economists have expressed concern that political paralysis would harm prospects of reducing Belgium's budget deficit, forecast at 4.8 per cent of gross domestic product in 2010.
Without the backing of the centre-right Open VLD, the remaining four parties in government still have 76 of the 150 seats in the lower house of parliament but it would be hard to govern with such a slim majority.
The Flemish liberal party said it had lost confidence in the government because of its failure to resolve a dispute between French- and Dutch-speaking parties over electoral boundaries around the capital, Brussels.
"We have not agreed on a negotiated solution and therefore Open VLD no longer has confidence in the government," Alexander De Croo, the party's chairman, said.
Leterme became prime minister for a second time last November when Herman Van Rompuy left the post to become president of the European Union.
Thursday's crisis occurred as Belgian politicians were due to vote on a controversial bill banning veils in public places.
The ban would include the full-face niqab and the burqa, a shapeless full-body cloak that covers the face with a fabric grille.
Those who ignore the ban could face a fine of up to $34 and/or a jail sentence of up to seven days.
If enacted, the bill would make Belgium the first European country to ban the garments.