By Sarah White

MADRID (Reuters) - Mariano Rajoy faces the first test of a tough second term as Spanish prime minister this week, as he unveils a new cabinet that must build cross-party support to pass reforms in a fragmented and hostile parliament.

The conservative leader won approval from lawmakers on Saturday to form a minority government after 10 months of political deadlock, but he will forced to seek out allies at every twist and turn to enact laws.

He is set to outline his team on Thursday under scrutiny over whether he will signal a fresh start by bringing in new faces, even if most are expected to come from within the ruling People's Party (PP).

Rajoy, who is due to be sworn in on Monday, governed with an absolute majority for four years from 2011. He lost that in 2015 and while the PP remained the largest party in parliament, he was unable to find coalition partners for a majority government, even after a fresh election in June this year.

Several of his ministers had major rows with the opposition, including during Rajoy's recent stint as caretaker prime minister. Rival forces had, for instance, called on acting interior minister Jorge Fernandez Diaz to resign in June over his links to an alleged smear campaign.

"In theory at least Rajoy will be obliged to show his government is somewhat different," said Carlos Barrera, a political communications professor at the University of Navarre. He noted, however, that the prime minister was not known for favoring abrupt changes.

Left-leaning newspaper El Pais, Spain's best-selling newspaper, called in an editorial on Sunday for a "deep renewal" of government members to build bridges with other parties.

After the two inconclusive elections since last December and months of infighting between parties, Rajoy's minority administration has pressing reforms and legislation to tackle.

First will be a new budget for 2017 to appease Brussels and meet next year's deficit targets, which will require either spending cuts or new formulas to raise extra revenues.

While the economy is recovering well, unemployment remains at almost 19 percent, the second highest rate in the EU after Greece.

Spain will also be trying to reclaim a spot at the European Union's top table as it deals with major problems, such as Britain's vote to leave the bloc. The caretaker government had been forced to take a back seat in recent months.

European Council President Donald Tusk called for unity in Spain. "I trust that over the next years and under your leadership, Spain will benefit from the political stability and social cohesion that are necessary to respond to the challenges at hand," Tusk said in a congratulatory letter to Rajoy on Sunday.

A FINE LINE

Many in Spain are skeptical about how productive the government can be with just 137 seats in the 350-strong parliament.

Even with support from the liberal Ciudadanos, Spain's fourth-largest party, Rajoy will struggle to achieve any form of stability without piecemeal agreements with the second-placed Socialists.

The center-left party reluctantly allowed Rajoy to return to office on Saturday by abstaining in a confidence vote, but has vowed to fight his policies.

Rajoy has called for dialogue with rivals but also laid down some red lines as opponents seek to reverse some of his previous reforms, such as a labor market overhaul that make it cheaper to hire and hire staff.

"I'm not prepared to undo what has been built. Things can no doubt be improved, but I cannot accept that they be demolished," Rajoy told parliament before Saturday's confidence vote.

His trump card is the threat of another snap election which would be likely to penalize his rivals. The Socialists, for instance, are without a leader and have angered many supporters by easing the PP's return to power.

Even so, Rajoy cannot afford to ignore the opposition like he did when he enjoyed an absolute majority, analysts said.

"Rajoy has to walk a fine line - he has to signal to his own voters that he is in control but also leave enough space to cut deals with other parties," said Antonio Barroso, an analyst with Teneo Intelligence in London.

(Editing by David Stamp)