In recent weeks he has also run into difficulties with his ruling coalition, with several nationalist lawmakers demanding changes to how the country issues residence permits in exchange for support for next year's budget.
Though Dombrovskis survived the standoff, he apparently felt the tragedy at the Maxima supermarket last week left his leadership too damaged to continue.
The announcement triggers the fall of the entire centre-right government. But it is not expected to cause a political crisis or disrupt the country's economy, which over the past two years was the fastest growing in the European Union.
Analysts say that in all likelihood Dombrovskis' party, Unity, will be part of the next coalition that will control the government until scheduled parliamentary elections next October.
Police have opened a criminal investigation into the cause of the tragedy, which also wounded at least 40 people. Possible explanations for the disaster include a flawed design, substandard construction materials and corruption.
There is "a feeling that he is perhaps a bit guilty for changes in the law which led to the problem," said political commentator Karlis Streips.
Many Latvians have expressed deep scepticism that the guilty parties will bear criminal liability and have gone so far as to demand that foreign engineers be invited to help the investigation.
Dombrovskis denied he was pressured and said that he had been mulling his resignation since the collapse, the country's worst disaster it declared its independence from the Soviet Union in 1991.
President Andris Berzins will appoint a new candidate based on who he believes could form a coalition that will receive the necessary majority approval by parliament.
Dombrovskis enacted harsh budget cuts and tax increases while at the same time implementing tough structural reforms demanded by international organizations, such as the International Monetary Fund, that put together a €7.5 billion rescue package for the country.
"Valdis Dombrovskis has been among the most successful of PMs in Europe," Swedish Foreign Minister Carl Bildt wrote in his Twitter account. "Took Latvia through difficult times. Charted the future."
Latvians were largely grateful for Dombrovskis' efforts, allowing him to be re-appointed twice as prime minister.
As part of the widely acknowledged recognition of Dombrovskis' achievements, earlier this year the European Central Bank and EU finance ministers gave their consent to Latvia's adopting the euro in 2014.
On January 1, Latvia will become the 18th member of the euro area.
- AP
