MILAN — Italy's president on Thursday set up a second round of talks to form a new government as the leaders of the two most successful parties in the last election vied to control the process despite lacking a parliamentary majority.

Even as both 5-Star Movement leader Luigi Di Maio and right-wing League leader Matteo Salvini pledged to open their own coalition talks with other political groups, President Sergio Mattarella did not formally tap either yet to form a new government.

After two days of talks in Rome, the Italian president said no political force had garnered enough support to sustain a stable government. He urged the country's three main political forces — the victorious 5-Stars Movement and the center-right, as well as the defeated Democratic Party -- to use the coming days "to responsibly evaluate the situation ... and the possible solutions to give life to a government."

Di Maio and Salvini staked their competing claims based on the fact that the 5-Star Movements was the party with the most votes in the March 4 election — 32 percent — while the center-right bloc that Salvini heads is the strongest political force, with 37 percent of the vote.

Di Maio told reporters after meeting with Mattarella that he would explore forming a government either with Salvini's League — excluding the other two parties in the center-right bloc — or with the Democratic Party, which has said its resounding electoral defeat places it in the opposition.

"The advantage of being a political force which is neither right- nor left-wing is to be free to talk with whomever really wants to do things," Di Maio said.

He said he would seek meetings with Salvini and Democratic Party leader Maurizio Martina to determine where there was the most convergence on programs, adding that he wanted to negotiate with a future partner a formal, signed coalition agreement as is traditionally done in Germany.

"We feel the responsibility to be the first political force of the country, and to work as quickly as possible to assure a majority for government of change that looks to the future," Di Maio said. He said the vote had made clear that Italians rejected any technical government or grand coalition of right and left.

Salvini left the door open to the 5-Star Movement as a coalition partner.

But he also presented the center-right bloc as a united entity, including Premier Silvio Berlusconi's Forza Italia, colliding with the 5-Star Movement's refusal to enter any coalition government with Berlusconi.

"We want to work for a government that will last five years, that has the national interests of Italy as a priority," Salvini said, adding that the numbers indicate the only solution is a center-right coalition with the 5-Star Movement.

"It doesn't take a scientist to realize that the other solutions would be temporary and improvised," Salvini added.

He said he will meet formally with other party leaders in the coming days to search for an agreement, starting with the center-right.

Earlier, Martina, the leader of Democratic Party said the center-left bloc would not play any role in Italy's new government.

With no clear path to agreement, Wolfango Piccoli of the Teneo Intel consultancy predicted it would be "a long and tortuous process" to form Italy's next government.

If an impasse persists through multiple rounds of talks, Mattarella can call for a new election — but analysts say most parties are eager to avoid that outcome.