US Defence Secretary Ashton Carter arrived in Madrid on Sunday, beginning a European tour amid alarm over Russian bombardments in Syria and the refugee crisis sparked by the conflict.

The trip comes at a fraught time for Carter, who started in the Pentagon's top job in February and who faces pressure at home over Syria and a simmering scandal involving military officials allegedly cherry-picking intelligence.

Adding to Carter's woes, a suspected US air strike on a hospital in the Afghan city of Kunduz killed 19 people Saturday.

The five-day trip to Spain, Italy, Britain and a NATO ministerial summit in Brussels is intended to recognise the work of ally nations as they scramble to tackle the refugee crisis as well as respond to Russian aggression in eastern Ukraine.

"It's a also a perfect reminder, especially given everything that Russia is doing right now, that the United States faces these threats in groups, in coalitions, in alliances," a senior US defence official said, speaking on condition of anonymity.

"It couldn't be more of a contrast to what we see Russia doing."

While in Spain, Carter will visit a base in Moron de la Frontera.

The Spanish senate last month approved the establishment of a permanent force of 2,200 US marines at the facility, which was initially bolstered in the wake of the 2012 attack on a US mission in Benghazi, eastern Libya.

The main mission of the Special-Purpose Marine Air-Ground Task Force Crisis Response (MAGTF) unit is to protect US embassies in Africa, evacuate civilians in difficulty, or intervene in conflicts or humanitarian crises.

It "was set up after Benghazi to give us a greater reach, flexibility and agility into threats emanating out of North Africa and the Middle East," the defence official said.

"It's just one of the symbols we have of how we are trying to deal with a new character of threats."

Carter, 61, has been on the job for eight months but unlike some of his predecessors -- such as Donald Rumsfeld and Robert Gates -- he has not established himself as a household name.

Carter has appeared reluctant to stray from official White House talking points and critics say he is overly cautious in his public pronouncements.

The Pentagon is under massive pressure over its efforts to intervene in Syria. While the White House does not want to commit ground forces to another difficult Middle East conflict, opponents are outraged by what they see as a lack of US action to halt the war that has claimed some 250,000 lives and displaced millions.

America leads a coalition of more than 60 nations conducting daily drone and plane strikes against Islamic State jihadists in Syria and Iraq, but is not targeting the regime of Syrian President Bashar al-Assad.

Russia this week started bombing Syria to support Assad, adding a bloody new geopolitical dimension to the humanitarian catastrophe.

The Pentagon is also trying to train moderate Syrian rebels to fight IS but the programme has been roundly denounced as a flop after some rebels gave ammunition to an Al-Qaeda-linked group and other fighters disappeared.

And a scandal has seen the Pentagon inspector general probe allegations senior military officials cherry-picked information to downplay the strength of the Islamic State group and Al-Qaeda's branch in Syria.

After Spain, Carter visits Sigonella in Italy, where a forward operating base for the MAGTF has been established. He will then meet leaders in Rome.

On Thursday, he travels to Brussels to attend a NATO summit expected to discuss Ukraine, Russia, Syria, Afghanistan and nuclear capabilities.

The US is helping train Ukrainian forces and has sent "non-lethal" military aid. On the ground, the security situation in east Ukraine appears to have improved in recent weeks with a truce between government troops and pro-Russian separatists largely holding.

Carter visits London for bilateral talks Friday with Britain's Defence Secretary Michael Fallon, to discuss the UK's ongoing Strategic Defence and Security Review.

He is also expected to discuss innovation. Carter, a physicist and a former Harvard University professor, has stressed the need for the US military to retain its technological edge.