The decision to delay presidential polls until at least late 2017 was part of a deal agreed in October by the government and fringe opposition groups that has been boycotted as a sham by the mainstream opposition.
The deal, which followed a "national dialogue", was aimed at calming soaring political tensions.
"I have offered my resignation as well as those of the members of my government... To respond to the spirit and the letter of the accord," said Matata as he left a meeting with President Joseph Kabila.
Kabila will address the situation Tuesday when he speaks to parliament to discuss "the state of the nation", according to a statement read on state media.
Vital Kamerhe, who led the fringe opposition bloc that participated in the national dialogue, is the favourite to succeed Matata as prime minister.
Following a meeting with Kabila, Kamerhe said that the nomination of a new premier was "imminent" and the formation of a new opposition-led government would be complete within a week.
The main dissident coalition Rassemblement (Gathering) -- which has rallied around veteran opposition leader Etienne Tshisekedi -- has rejected the deal that followed the "national dialogue" and stepped up its calls for Kabila to leave office by December 19 when his term ends.
The country has been in a state of crisis since disputed elections in 2011 returned Kabila to office for a second term.
A 2006 constitutional provision limits the presidency to two terms.
Violent anti-Kabila protests on September 19 and 20 triggered by the political instability claimed 53 lives, according to the UN.
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