Poroshenko called for General Prosecutor Viktor Shokin to resign and said: "The same parameters should be applied to the government also ... society has clearly decided that there have been more mistakes than achievements, and denied ministers its trust."
Speaking in parliament after the statement, Yatseniuk was not explicit about whether he would resign or not, saying he would accept whatever decision parliament made. Shokin did tender his resignation, however, the newspaper Ukrainska Pravda reported.
Poroshenko heads Ukraine's largest party, and Yatseniuk the next largest. Both are in the ruling coalition.
Maksym Burbak, the parliamentary leader of Yatseniuk's party, told lawmakers that the consequences of voting against the government would be felt "literally the next day - since this could trigger early elections and chaos".
If the government collapsed, it would dismay Ukraine's international backers, who have invested much cash and political capital supporting the government in its standoff with Moscow after Russia's annexation of Crimea in 2014.
Ukraine's failure to tackle corruption and implement reforms has already derailed a Western aid programme that keeps its war-ravaged economy afloat.