MOSCOW, Jan 16 (Reuters) - Russia is ready to resume cooperation with the United States on security issues such as the fight against terrorism and cyber crime, a close ally of President Vladimir Putin said, days before the inauguration of Donald Trump as president.

Trump, who has praised Putin as "very smart", has signalled he wants to improve strained ties with Russia, despite U.S. intelligence agencies alleging the Kremlin chief ordered a cyber campaign to discredit rival Hillary Clinton during the 2016 presidential race. urn:newsml:reuters.com:*:nL1N1EW0ZW

Russia denies it tried to sway the U.S. election by hacking or other means and Trump has played down the allegations. Last week, he also dismissed accusations that Moscow had collected compromising information about him as "fake news" and "phoney stuff".

In an interview published on Monday, Nikolai Patrushev, secretary of Russia's Security Council, struck a cautiously positive tone on the prospects for collaboration with Washington after a period of icy relations under Barack Obama.

"If Donald Trump's administration is interested we will be ready to resume full-format consultations with our American partners through the Russian Federation's Security Council," Patrushev told the government-controlled daily Rossiiskaya Gazeta.

However, Patrushev added that he did not expect rapid improvements or a swift lifting of sanctions he said the West had deliberately imposed to "hold Russia back" because the two sides were starting from such a low base.

Patrushev made his comments before Trump told Britain's Sunday Times in a weekend interview that he would propose offering to end sanctions imposed on Russia over its annexation of Ukraine's Crimea region in return for a nuclear arms reduction deal with Moscow. urn:newsml:reuters.com:*:nL5N1F50VI

On Monday the Kremlin said it would wait until Trump takes office on Friday before commenting on any proposals. urn:newsml:reuters.com:*:nR4N1EP02Q

Any agreements to resume cooperation would have to be guided by the principles of mutual respect and equality, said Patrushev. Putin himself chairs Russia's Security Council.

Trump has said Russia can be an important ally against militant Islamist groups such as Islamic State.

Patrushev said he believed the Obama administration had deliberately tried to discredit Russia because it was unwilling to accept that Washington's position of global leadership was slipping. Obama has been strongly critical of Russian policy in Ukraine and in Syria.

In excerpts from Patrushev's interview released on Sunday, he told Rossiiskaya Gazeta that Russia was facing increased cyber attacks from abroad - turning against Western countries their own charges of Russian meddling in their affairs. urn:newsml:reuters.com:*:nL5N1F50CC

(Reporting by Andrew Osborn; Editing by Gareth Jones) ((andrew.osborn@thomsonreuters.com; +7 495 7751242; Reuters Messaging: andrew.osborn.thomsonreuters.com@thomsonreuters.net))