MOSCOW, July 21 (Reuters) - Russian President Vladimir Putin has approved a law which will tighten controls on civil rights groups funded from abroad, the his press office said on Saturday, a step opponents say is part of a campaign to suppress dissent.

The law, which was cleared by the upper house of parliament earlier in July, will force non-governmental organisations (NGOs) engaging in "political activity" to register with the Justice Ministry as "foreign agents" and to file a report to officials every quarter.

Opposition groups say Putin is trying to silence groups whose criticism of his human rights record has undercut his credibility and helped fuel seven months of protests against his rule, the biggest since he came to power in 2000.

Putin, a former KGB spy, has dominated Russia for 12 years as prime minister or president and he won another six-year stint in March.

Earlier this month, the U.S. State Department voiced "deep concern" about the NGO law - and was promptly rebuked by Moscow for "gross interference", an exchange that underlined the impact the bill has had on already strained relations.

Putin said on Thursday that laws to open up competition in Russia's political system must be implemented with care, suggesting he remains wary about reforms introduced after the wave of protests.

In April then-president Dmitry Medvedev signed off on a law that eased regulations on the registration of political parties, cutting the required number of members in a party to 500 from the previous 40,000.

The law was aimed at appeasing demonstrators who had taken to the streets after accusations of voting fraud in a parliamentary election in December which gave the Putin-supported United Russia party a slim parliamentary majority.

"It is necessary that the laws which were passed on a legislative level make their way into society correctly, peacefully and in accordance with the letter and spirit of the law," said Putin.

"But in no case (may they) allow any destructive forces to shake up the situation or moreover allow them (to do so) in a destructive-terroristic way." (Writing by Andrey Ostroukh; Editing by Mark Heinrich)