"During this critical time for the United States, NATO and the European Union, the US Congress and the American people look forward to your message of friendship and partnership, as we work together to strengthen our critical alliance and advance a future of peace around the world," Pelosi wrote the 29-member organization's secretary general Jens Stoltenberg.
The top Democrat said the invitation was made on behalf of Democrats and Republicans in Congress.
The invitation comes amid trans-Atlantic tensions. Trump has been unstinting in his criticism of NATO's European members, accusing them of freeloading on the protection offered by the US military while not spending enough on their own armed forces.
A NATO summit last July jangled nerves when Trump reportedly threatened to "go it alone" unless allies boosted their spending.
Before taking office Trump called NATO "obsolete" and soon after July's summit he questioned whether the US would honour the alliance's founding principle of mutual defence for newest member Montenegro.
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