Poland's president urged US President-elect Donald Trump to keep Washington's promise to deploy troops on NATO's eastern flank amid tensions with Russia.

"Polish-American relations have become an important pillar of the European and transatlantic stability," Polish President Andrzej Duda said in a letter of congratulations.

"We are particularly pleased that during this year's NATO Summit in Warsaw the US decided to increase its military presence in Poland, thereby strengthening the Alliance's Eastern flank.

"We sincerely hope that your leadership will open new opportunities for our cooperation based on mutual commitment."

Trump, a real estate mogul-cum-reality TV star, sparked ire in July among eastern NATO members ruled by Moscow during the Soviet era when he questioned the alliance's key collective security guarantee.

As part of that commitment, NATO leaders endorsed plans this summer to rotate troops into Poland and the three Baltic states to reassure them they would not be left in the lurch if Russia was tempted to repeat its 2014 Ukraine intervention.

The US-led battalion that will begin operations next year in Poland will be stationed near the border with Russia's Kaliningrad exclave.

The US also said in March it would deploy an additional armoured brigade of about 4,200 troops in eastern Europe from early 2017 on a rotational basis.

Moscow has stepped up its presence in the Baltic Sea area. Its jets regularly violate the airspace of smaller ex-Soviet NATO allies like Estonia and in April they even buzzed a US naval destroyer.

Last month Poland criticised Moscow's deployment of nuclear-capable Iskander missiles into its Kaliningrad outpost that borders NATO members Poland and Lithuania.

It also denounced as "aggressive and irresponsible" Russia's subsequent deployment of two warships in the Baltic Sea capable of launching long-range nuclear warheads.