MADRID (AP) — Spain's incumbent conservative Prime Minister Mariano Rajoy turned down an offer Friday by King Felipe VI to try to form a new government following last month's inconclusive elections but said he would continue to seek support for his candidacy as premier.

More time is needed for negotiations, Rajoy said, but added it didn't make sense for him to present himself at the moment because the vast majority of deputies were certain to vote against him in Parliament.

"I haven't given up on anything," he said after meeting with Felipe at the end of a week of talks between the king and party leaders. "I didn't say 'no' to my investiture, I conveyed to him (the king) that I didn't have enough support yet."

Rajoy's Popular Party won 123 seats in the Dec. 20 election, which was more than any other group but not enough to garner a majority in the 350-seat lower house of Parliament. It was also way below the 186 seats it held following the previous general election in 2011.

Felipe could now call on opposition Socialist party leader Pedro Sanchez. The Socialists came second in the election with 90 seats and appear to have more chances of mustering support from other groups in Parliament.

The palace said the king will begin fresh talks with party leaders next Wednesday in a bid to find a candidate.

The nominated candidate must win a vote of confidence in Parliament. If no party leader manages to win Parliament support within two months of the first vote, fresh elections must be called.

For weeks, Rajoy has sought to head a minority government with the support of the Socialists and the center-right newcomer Ciudadanos, which got 40 seats. But the Socialists have said they intend to vote against him no matter what.

In contrast, Sanchez earlier Friday received an offer by the radical leftist Podemos group to form a coalition government. Sanchez said that Rajoy should have a first shot but that the Socialists intend to try to form a government if he fails.

Podemos leader Pablo Iglesias said he wants the Socialists, Podemos and the smaller United Left to build a "government of change," with Cabinet positions allotted in accordance with the results of last December's election. Iglesias suggested he could be deputy prime minister in a Sanchez-led government.

Newcomer Podemos and its allies came third in the election with 69 seats. The United Left has two.

"We have decided to seize the initiative and take a step forward," Iglesias told reporters after meeting the king. "There is no more time for hesitation. Either you're for change or for stagnation and impasse."

However, the Popular Party and Ciudadanos have said they would seek to block such a coalition.

Rajoy's popularity has plunged over the past four years in government chiefly because of party-linked corruption scandals, unpopular laws and austerity measures brought in to help get Spain out of a severe economic crisis.

The December election produced Spain's most fragmented Parliament in decades and ended the alternating grip on power the Popular Party and Socialists have had. The strong emergence of Podemos and Ciudadanos was interpreted as a sign that Spaniards wanted change.

Hatton contributed from Lisbon, Portugal.