The threat of the Islamic State (Isis) has topped President-elect Donald Trump's list of defence priorities. However Russia, a major concern for both Nato and top Pentagon officials, fails to make the list.

In a leaked Department of Defense memo, Trump transition team member Mira Ricardel is said to have laid out the president-elect's number one defence priority as developing "a strategy to defeat/destroy Isis".

The second objective is to eliminate defence spending caps introduced by President Barack Obama and build up the American military's "strength/size/readiness." Other priorities in the memo, obtained by Foreign Policy magazine, include a "cyber strategy" and finding "greater efficiencies" in the department.

Russia's absence in defence objectives, and Trump's focus on defeating Isis, mirrors statements made by a senior member of the president-elect's foreign policy team over the weekend. They told London's Sunday Times that Trump's policies will be "night and day" compared to those of President Barack Obama.

Trump will start off with "high-profile military actions" against Islamic extremists in the Middle East to announce there is "new sheriff in town", they said. Trump will order his generals to draw up a plan 30 days from his inauguration to defeat Isis. When it comes to Russia Trump intends to woo its President Vladimir Putin with "prestige" and photo ops, the official said, to give "the US tremendous leverage",

But the United State's closest Nato allies and top members of the Pentagon see Russia as a bigger threat than Isis.

On Monday (19 December) Nato's Secretary General, Jens Stoltenberg, met with Russian officials. Stoltenberg said the 28-country military alliance of mainly European nations "will not recognise Russia's illegal and illegitimate annexation of Crimea" in 2014.

The situation in eastern Ukraine "remains of deep concern", Stoltenberg said of increased fighting and ceasefire violations there. A new report by journalist Eliot Higgins released 21 December examines the "massive scale" of Russia's artillery bombardments in eastern Ukraine.

Nato is pushing for economic sanctions imposed by Europe and the US on Russian officials and companies to remain in place. However Trump spoke out against the sanctions during the 2016 campaign. His pick for secretary of state, Exxon Mobile CEO Rex Tillerson, has also spoken against the sanctions.

Pentagon generic image
The Pentagon building, headquarters of the United States Department of Defense (DOD) in Washington, DC, 26 December 2011 STAFF/AFP/Getty Images

In recent weeks concern about Russia has been raised inside the Pentagon after the CIA and FBI concluded Putin sought to influence the election. The intelligence community believes he supported Trump through a series of hacked document leaks. Obama has launched a bipartisan review of those claims.

"If you want to talk about a nation that could pose an existential threat to the United States, I'd have to point to Russia," said America's senior most military officer, General Joseph Dunford, chairman of the US Joint Chiefs of Staff, during his confirmation hearing on 9 July 2015. "If you look at their behaviour, it's nothing short of alarming," he added. China, North Korea, and Isis were the next largest threats, he said — in that order.

"From a military perspective it's reasonable that we provide that support to the Ukrainians," Dunford said.

The leaked memo indicates that Trump administration officials have been briefed on counter-Isis, China and North Korea, with more briefings being scheduled. However, a Pentagon spokesman told Foreign Policy that Trump's defence transition team have been briefed on Russian issues.