* Gul also hints he will not block judiciary bill
* Laws have sparked fight in parliament, protests
* Opposition plans appeal to constitutional court (Recasts with Gul approving Internet law)
By Nick Tattersall
ISTANBUL, Feb 18 (Reuters) - Turkish President Abdullah Gul approved a new law tightening control of the Internet on Tuesday in a move bolstering embattled Prime Minister Tayyip Erdogan but raising concerns about free speech.
The legislation, along with a law increasing government influence over the judiciary, is seen by Erdogan's critics as an authoritarian response to a corruption inquiry shaking his government, a bid to stymie court cases and to stop leaks circulating online.
The judiciary bill will give the government more say in the naming of judges and prosecutors, while the Internet law will enable the authorities to block access to web pages within hours without a prior court order.
Gul said he gave his approval for the Internet law after the government said it would push through parliament amendments of the legislation in response to the president's concerns regarding two articles in the law.
"In order to give the opportunity for these amendments to be made rapidly, I approved the law in front of me as soon as I returned from Hungary," Gul wrote on his Twitter account.
The moves by Turkey, which has been seeking membership of the European Union for decades, have raised concern in Brussels, which fears it is shifting further away from EU norms. They have also unnerved investors in a country whose stability over the past decade has been based on Erdogan's firm rule.
The government says the laws will further democracy by taking back control of a judiciary it sees as influenced by a powerful but unaccountable cleric bent on unseating Erdogan, and by protecting individuals' privacy on the Internet.
Police fired teargas to disperse demonstrators protesting against the Internet law in Istanbul this month and parliamentarians debating the judicial reforms came to blows on Sunday, leaving one with a broken nose.
Communications Minister Lutfi Elvan said earlier on Tuesday evening the government would present to parliament the Internet law amendments once Gul had given his approval.
Under the changes, permission for authorities to access Internet traffic data will require a court order. Telecom authorities will have to seek a court ruling within 24 hours if they block access to Internet material on privacy grounds.
Gul has made little secret of his desire to return to mainstream politics and is seen as a future leader of the AKP, an ambition his critics say leaves him too wary of conflict with Erdogan to act as an effective check on his power.
"Gul wants to serve as president for a second term and has the desire to chair the AKP after Erdogan, so even if he does not fully agree, he is approving controversial regulations from the party," political analyst Atilla Yesilada said in a report.
The battle for control of the High Council of Judges and Prosecutors (HSYK), which appoints senior members of the judiciary, lies at the heart of a feud between Erdogan and influential U.S.-based cleric Fethullah Gulen.
Gulen, whose followers say they number in the millions, is believed to have built up influence in the police and judiciary over decades and leads a powerful worldwide Islamic movement from a forested compound in the United States.
Erdogan blames Gulen, a former ally who helped cement AK Party support over the past decade, for unleashing the graft investigation he sees as an attempted "judicial coup" meant to undermine him in the run-up to local and presidential elections this year. The cleric denies any such role.
Gul is seen as enjoying more support from Gulen's network of sympathisers, who have more pro-democratic and reformist views, than does Erdogan, whose stand on issues from abortion to alcohol they see as unnecessary interference in private life.
But Gul has also been critical of the cleric's influence in state institutions in recent months, echoing Erdogan's warning that a "state within the state" will not be tolerated.
In the eyes of Turkey's opposition, too weak in parliament to stall AKP bills, that opens the way for Erdogan to impose an increasingly authoritarian rule.
"If the president approves the HSYK law, the judiciary will be bound completely to the government. The separation of powers will be completely shelved," said Devlet Bahceli, head of the opposition Nationalist Movement Party (MHP).
"I fear that Prime Minister Erdogan will sit at the top of the judiciary as the chief judge." (Additional reporting by Asli Kandemir and Daren Butler; Editing by Tom Heneghan)