If he finds backing among the parties, Dombrovskis will then need to win a vote of confidence in parliament.
Dombrovskis said Latvia needed budget cuts worth $1.26bn, on top of spending reductions of $9.55bn which were agreed to win a bailout last year from the International Monetary Fund (IMF) and the European Union.
He said: "In reality the state is on the verge of bankruptcy. The receipt of further financial support depends on budget amendments being passed soon, on the budget deficit being reduced to the level agreed [with the IMF and EU]".
IMF and EU officials said they had suspended talks with Latvia until a new government was in place, and to let a new coalition respond to issues the fund had identified.
Christoph Rosenberg, the IMF's Latvia mission chief, said: "This is an ongoing process, the economic conditions are changing constantly, globally and in Latvia. The programme has to be constantly adjusted to that."
Latvia's finance ministry has forecast that the economy will shrink 12 per cent this year, much worse than the 5 per cent fall forecast when Latvia agreed the bailout.
Ratings agency Standard & Poor's downgraded Latvia's debt to junk level on Tuesday, the second EU state after Romania to fall below investment grade.
The economic crisis has prompted some economists to say Latvia should abandon the fix of its lat currency to the euro but Dombrovskis rejected this.
"I do not support a devaluation of the lat in the current situation," he said.
Zatlers said he nominated Dombrovskis because the four parties in the outgoing coalition as well as another smaller centre-right opposition party had said they would support him.
Karlis Streips, a political commentator, said: "I think the main challenge first of all will be to simply put a government together.
"Latvia needs a government which will work in favour of the people and not just a few private individuals."