The Kremlin has denied rumours that President Vladimir Putin is seriously ill, after he had to cancel a number of engagements this week.

Footage of the president working from his residence outside Moscow was released on Russian state television today, although it has not been independently verified.

In the brief footage Putin is shown in his office at his Novo-Ogaryovo residence, where he conducts many of his meetings, sitting across a table from Supreme Court head Vyacheslav Lebedev, discussing the justice system.

Putin was due to visit the Kazakh capital, Astana, this week for a meeting with the presidents of Kazakhstan and Belarus, but the trip was postponed at short notice.

Although some photos and footage have been uploaded onto the Kremlin's website this week, Putin has not been seen in public since March 5, leading to suggestions that the Kremlin was trying to cover up the president's ill-health. The photos have been subjected to detailed scrutiny with people examining the date on his desk calendar and his clothes to try to work out when the photos were taken.

A treaty-signing ceremony was also cancelled, leading to feverish speculation on Russian social media on Thursday – though most mainstream organizations, which are deferential to the Kremlin, steered clear of the issue.

Presidential spokesman Dmitry Peskov responded by saying that those making the claims had caught "spring fever", the state-run news agency Itar Tass reported.

"As soon as the sun comes out in the spring, as soon as spring starts to smell, begin aggravations," Peskov said.

"We take these annoyances quietly, and patiently answer all of the questions," he added.

Peskov told Reuters on Thursday that Putin, who is 62, was in good health and was working as usual.

The rumours fed into an atmosphere among Moscow's political classes that was already more than usually febrile because of the conflict in Ukraine, and the February 27 killing of opposition leader Boris Nemtsov.

There was no hard evidence that Putin was ill, or that there was any crisis inside the Kremlin. Markets were unruffled by the rumours. The rouble strengthened slightly on Monday, after the central bank cut rates by one percentage point, slightly less than some analysts had expected.

Additional reporting by Reuters