Kiev (AFP) - NATO chief Jens Stoltenberg pledged support for Ukraine during a visit to Kiev on Monday, as the ex-Soviet republic battles a bloody insurgency by pro-Russian separatists in the east.

More than 10,000 people have been killed since a Russian-backed rebellion against the pro-EU government in Kiev erupted in April 2014.

Ukraine and the West accuse Moscow of smuggling weapons and troops across the porous border in support of the separatists, a charge has repeatedly denied.

"Russia has maintained its aggressive actions against Ukraine, but NATO and NATO allies stand by Ukraine and stand on your side," Stoltenberg said at the NATO-Ukraine Commission session in Kiev.

"Russia must withdraw its thousands of soldiers from Ukraine and stop supporting the militants," he added during a press conference with Ukrainian President Petro Poroshenko.

The conflict in eastern Ukraine and Russia's annexation of Crimea in 2014 have driven ties between Moscow and the West to their lowest point since the Cold War.

"We are also here to demonstrate NATO's solidarity with Ukraine and our firm support for the sovereignty and territorial integrity of your country," Stoltenberg said.

"NATO allies do not and will not recognise Russia's illegal and illegitimate annexation of Crimea."

The NATO chief's trip came a day after US Secretary of State Rex Tillerson made a maiden visit to Kiev and urged Moscow to take the "first step" to ease the conflict in Ukraine's east.

The US and the European Union have imposed sanctions on Russia, although Moscow has denied backing the rebels.

- Path to membership? -

Ukraine sees NATO accession as a way to bolster its defences against former master Moscow.

In June, Ukraine's parliament voted to back attempts by the nation to seek membership of the 29-member bloc.

It approved legal amendments enshrining membership in NATO as a foreign policy priority.

But the Kremlin has long been angered by NATO expansion into what Moscow views as its sphere of influence in the former Soviet region.

Story continues

"It (Ukraine's rapprochement with NATO) will not contribute to the strengthening of stability and security on the European continent," Kremlin spokesman Dmitry Peskov said.

Moreover, Kiev has yet to officially apply to start the lengthy and politically challenging process of joining the US-led alliance.

Poroshenko explained that embattled Ukraine was eager to join the bloc, but painful political and economic reforms need to be implemented before the country was ready to lay out its claims on membership.

"We are determined to reforms... to meet the membership criteria," Poroshenko told journalists.

"NATO will continue to support Ukraine on the path towards closer relationships with NATO," Stoltenberg added.