MOSCOW: US President Barack Obama concluded his trip to Moscow on Wednesday, having met Russian leaders and signed a handful of security deals in his mission to heal badly strained relations with Moscow.

The US presidential plane flew out of Moscow, as Obama headed on to Italy for a meeting of the G8.

Obama and his wife Michelle waved to reporters after climbing aboard with their daughters Sasha and Malia.

In a minor technical mishap, the stairs vehicle that the Obamas climbed then failed to start, and workers at Moscow's Vnukovo-2 airport needed to push it away manually before the plane could depart.

Earlier, United Nations Secretary General Ban Ki-moon hailed an agreement on nuclear disarmament that Obama had signed with his Russian counterpart Dmitry Medvedev during the summit.

"The Secretary General believes that this agreement will make a significant contribution to the process of nuclear disarmament, as well as nuclear non-proliferation," said a statement from the UN chief's office.

The agreement -- a roadmap for replacing the 1991 Strategic Arms Reductions Treaty, which expires in December -- was a key achievement of the summit, along with a deal on the transit of US supplies to Afghanistan.

But Obama's visit failed to fix other problems, including a dispute over a US missile shield in eastern Europe.

Russian newspapers on Wednesday focussed on Obama's breakfast meeting with strongman Prime Minister Vladimir Putin and on the US president's speech on US-Russian relations the day before.

"The order to be friends has been given," the Kommersant daily said in its front-page headline, commenting on the meeting with Putin, the former president who is still widely regarded as holding the real power in Russia.

"The second day of Obama's visit, like the first, proved that Russian-US relations have genuinely begun changing for the better," wrote official government newspaper Rossiiskaya Gazeta.

"In the voice of the US guests, no longer is there is a tone of mentoring, nor is there a desire to talk down to their Russian colleagues," said the newspaper, commenting on Obama's speech.

In his address, which was billed as a major foreign policy address building upon previous speeches in Cairo and Prague, Obama reached out to Russians distrustful of the United States.

"America wants a strong, peaceful, and prosperous Russia," Obama told an audience of graduating students from an elite Moscow economics school.

He acknowledged the difficulties in forming a lasting partnership between the two former Cold War enemies, but said Russia and the United States now shared common interests on the main issues of the 21st century.

But Obama also praised democratic freedoms -- a sensitive topic for Putin and Medvedev, who have been criticised for being undemocratic -- and said that Russia had to respect the sovereignty of its neighbours Georgia and Ukraine.

US-Russian relations were badly strained under the administration of Obama's predecessor, George W. Bush, amid disputes over the missile shield and last summer's war between Russia and Georgia.

Obama had vowed to "reset" those relations after his inauguration in January.