MADRID (Reuters) -Spain's King Felipe on Tuesday nominated acting Prime Minister Pedro Sanchez to face a parliamentary vote for a new mandate after his conservative rival failed in his bid to become premier last week, lower house speaker Francina Armengol told reporters.

Sanchez said he would start talks with the main parties on Wednesday, "without wasting time", and starting with his Labour Minister Yolanda Diaz, the head of leftist Sumar.

In an inconclusive general election on July 23, Sanchez's Spanish Socialist Workers Party secured fewer seats than the conservatives of Alberto Nunez Feijoo, but Sanchez has been adamant that he can muster enough support for his candidacy.

"I've accepted the task given to me by the head of state... I am willing to work to form as soon as possible a progressive coalition government with enough support to guarantee the stability that the country needs," Sanchez told reporters.

To reach the threshold of votes needed to stay in office, he will have to woo Catalan and Basque parties, some of which advocate their regions' independence from Madrid.

Addressing the divisive issue, Sanchez said one of his government's main pillars would be working for the coexistence and concord between Spaniards, especially in Catalonia.

Armengol said Sanchez was yet to share with her his suggested schedule for the investiture vote.

If no candidate secures a majority by Nov. 27, a repeat election has to be called.

(Reporting by David Latona, Belen Carreno Emma Pinedo and Inti Landauro, editing by Andrei Khalip)