MILAN, Feb 2 (Reuters) - Italian oil services group Saipem said on Tuesday it would appeal an Algerian court ruling ordering one of its units to pay a 34,000 euro ($37,104) fine for allegedly inflating prices on contracts to build a gas pipeline.

The market is closely monitoring Saipem's various legal cases, hoping for signs of reprieve after a fall in orders as oil majors cut investments following a slump in the oil price.

The company, which is jointly controlled by oil major Eni and state lender fund FSI, is also in the midst of a highly-dilutive 3.5 billion euro rights issue as it seeks to turn its business around and ensure survival.

Algerian state energy firm Sonatrach awarded a Saipem unit the contract to build a gas pipeline called GK3 in 2009. The contract was worth about 433.5 million euros, according to Saipem's rights issue prospectus.

Saipem said on Tuesday the court of Algiers alleges that Saipem Contracting Algerie inflated prices "on contracts awarded by a public company engaged in industrial and commercial activities, taking advantage of the authority or influence of representatives of said company".

The Italian group denied any price inflation above market rates occurred and expects the payment of the fine to be suspended once it has presented its appeal.

The company added that the court had granted Saipem's request to unfreeze two of its bank accounts, which have been blocked since 2010 in connection with the trial and which hold the equivalent of around 82 million euros.

Saipem said Sonatrach had reserved the right to claim payment of damages it allegedly suffered in a separate civil proceeding, but no such claim had been presented so far.

The company's legal problems in Algeria are not limited to the GK3 contract.

In October, Saipem and five people were ordered by a Milan judge to stand trial on charges it paid intermediaries 197 million euros to win contracts worth 8 billion euros with Sonatrach.

Saipem said at the time there were no grounds for the company to be held liable.

Among Saipem's other legal disputes is the cancellation by Gazprom of the South Stream gas pipeline project which Saipem had won contracts to build. In its rights issue prospectus the contractor said it was asking the Russian energy giant to pay it 760 million euros for termination of the contract. ($1 = 0.9163 euros)

(Reporting by Agnieszka Flak and Stephen Jewkes; Editing by Alexander Smith) ((agnieszka.flak@thomsonreuters.com; +39 02 6612 9450; Reuters Messaging: agnieszka.flak.thomsonreuters.com@reuters.net))

Keywords: SAIPEM ALGERIA/