MADRID (Reuters) - King Felipe VI will hold a formal round of talks with Spain's political parties next week for the fourth time in a seven-month-old power deadlock, his office said on Thursday, as parties struggle to form a coalition administration.

This time around, the king is widely expected to propose acting Prime Minister Mariano Rajoy as a candidate to try and form a government.

Rajoy's center-right People's Party (PP) won most of the votes in June, but fell 39 seats short of the majority he needed to govern, the second general election in six months to prove inconclusive.

King Felipe will meet the PP, the Socialist Party, the left-wing Unidos Podemos and liberal Ciudadanos on July 28, and the smaller, regional groups, which include Catalan and Basque separatist parties, on July 26 and 27, his schedule showed.

Rajoy on Wednesday edged potentially closer toward forming a government after cutting a deal with his most likely partner, liberal newcomers Ciudadanos, to elect one of his ministers to the post of parliament speaker.

"For my part, I am ready to govern. I'm aware of the responsibility that I have," Rajoy told reporters on Wednesday.

However, such a pact would still fall short of the seats needed to form an administration.

When a party wins fewer than the 176 seats needed to control the lower house of the 350-strong parliament, under Spanish law, the king holds talks with all parties across the political spectrum and proposes a candidate to become prime minister.

The candidate will then submit a viable proposal for government to a confidence vote in parliament in which they must secure an absolute majority to avoid a second vote 48 hours later.

King Felipe has already held three such consultations since the first election in December, of which two resulted in no proposal and one in the nomination of Socialist Party leader Pedro Sanchez, who did not pass the confidence vote that ensued.

(Reporting by Amanda Cooper, Editing by Sonya Dowsett and Angus MacSwan)