By Joachim Dagenborg

SUNDVOLLEN, Norway (Reuters) - Norway's center-right parties agreed on the terms of their coalition government on Monday, promising to lower taxes, reduce the economy's reliance on the vast oil sector, invest heavily in infrastructure and curtail immigration.

The Conservatives, led by prime minister-designate Erna Solberg, and their smaller ally, the populist Progress party, cleared one of the last major hurdles with the deal, paving the way for the two to take power on October 18 after winning elections last month.

"There are areas where we disagree but fewer than many would have believed," Solberg, 52, told a news conference. "Even though Norway is a fantastic country, some people fall through the safety net. ... we will try to plug the holes."

Solberg's government will rule in a minority after failing to win over several small centrist parties. But minority governments are common in Nordic countries and the Conservatives have enlisted the formal outside backing of the Liberals and the Christian Democrats to ensure stability.

The deal, which did not divide up cabinet posts, also puts the anti-immigration and anti-tax Progress Party in government for the first time in its 40 years - a big shift for a party that has spent years softening its image and was until now considered too radical for government.

The new coalition is to maintain restraint in spending oil money, upholding the current spending cap, but officials said there was some leeway under the rule and it would lower taxes for the average wage earner, gradually wind down the wealth tax and abolish the inheritance tax.

Keeping to promises of increased infrastructure investments, the coalition parties also agreed to set up an extra-budgetary fund for projects like road and rail building to the tune of 100 billion crowns ($16.75 billion) over the next five years.

In oil policy, the government promised to keep offering new areas for exploration to energy firms, a major demand from the sector, but will keep several environmentally sensitive Arctic regions closed to exploration.

Coalition parties also promised to strengthen Petoro, the state holding firm that owns minority stakes in most oil licenses, by providing it more cash, and said they would prioritize enhanced recovery as Norwegian fields mature.

In immigration, the parties agreed to tighten asylum rules, limit the appeals process and make it easier to deport asylum seekers.

Although both parties said they would consider breaking up Norway's $790 billion oil fund, the world's biggest sovereign wealth fund, their platform stopped short of such a move and instead promised a review.

(Additional reporting by Alister Doyle; Writing by Balazs Koranyi; Editing by Mark Heinrich)