ITV News Correspondent Juliet Bremner reports
As he announced his resignation in Italy's parliament, Mr Conte blamed the collapse of his government on his anti-migrant interior minister, who triggered a political crisis to try to force early elections.
Addressing the Senate, Mr Conte blasted Matteo Salvini for setting in motion a "dizzying spiral of political and financial instability" by essentially pulling the plug on the government.
Mr Salvini's right-wing League party sought a no-confidence vote against Mr Conte earlier this month, a stunningly bold move for the government's junior coalition partner.
Mr Conte, a lawyer with no political experience who was tapped to break a post-election stalemate last year, handed his resignation to President Sergio Mattarella at the presidential palace.
President Mattarella - who is head of state - has said he will hold talks with the constantly clashing coalition government about Italy's future, including exploring options that may involve forming a coalition that has the support of a new majority in parliament.
If the collaboration proves impossible, the president will dissolve parliament and call for an early election, which could happen as early as October.
In the coming months, the government will also need to make budget cuts to keep in line with EU financial regulations, something closely monitored by Brussels.
Mr Salvini, who sat next to Mr Conte during his speech, smirking at times, declared, "I'd do it all again".
He repeatedly kissed a rosary he slipped out of his pocket right after Mr Conte rebuked him for associating "political slogans with religious symbols".
Pressing for elections as soon as possible, Mr Salvini said: "I don't fear Italians' judgment."
In the European Parliament election three months ago in Italy, as well as in current opinion polls, Mr Salvini's League party has become the major political force among Italians.
His crackdown on migrants, whom the party's voter base largely blames for crime, appears to be a huge factor in Mr Salvini's climbing popularity.
Early elections would pull the plug on Parliament three years ahead of schedule, perhaps as soon as late October.
Should any early elections sweep Mr Salvini into power, financial markets could be rattled by his Euro-scepticism.
Depicting himself in counterpoint to Mr Salvini's often derogatory depiction of European Union rules, Mr Conte said: "I tried in these 14 months to guide Italy's policy along the path of a critical pro-Europe line, but always oriented constructively."
The current coalition government is formed by two rivals: Luigi Di Maio's anti-establishment 5-Star Movement, and Mr Salvini’s Eurosceptic, anti-immigration League party.
Both men are deputy prime ministers.
Mr Salvini’s League party has always held a hard-right and hard-line stance against immigration.
In fact, Sicilian Prosecutor Luigi Patronaggio is investigating whether he can potentially hold Mr Salvini on charges of kidnapping, after the interior minister refused to allow 80 migrants stranded on a boat to shore, despite offers from six countries to take them.
The migrants - stuck on the Spanish rescue ship Open Arms for over 19 days - grew so frustrated that on Tuesday, 15 jumped in the sea to escape the vessel and attempted to swim to shore.
With the help of Italian rescue workers, the swimmers reached the shores of the nearby Italian island of Lampedusa.
Spain tried to end the spiralling humanitarian crisis by dispatching a naval ship to escort the Open Arms back to Spain.
However, Open Arms said that would make operations on board “desperate” and “intolerable” for the remaining migrants.