Haley told UN Security Council members that Washington won't waver in supporting the NATO military alliance and "looks forward to improving our cooperation" with the European Union.
"The United States may, from time to time, disagree with EU perspectives, as friends do," she said, but "no one should interpret occasional policy differences and debates as a signal of anything less than total commitment to our alliances in Europe."
Some European leaders have been on edge about Trump, who once called NATO "obsolete," has been supportive of Britain's vote last year to leave the 28-nation EU and has taken aim at multinational trade deals.
Since becoming president, Trump has tempered his rhetoric about Russia and stressed the importance of NATO during telephone conversations with multiple foreign leaders.
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In recent days, Vice President Mike Pence and other high-ranking members of Trump's administration have been in Europe pledging America's continued partnership with its allies and continued pressure on Russia to do its part to end fighting between Ukrainian forces and Russia-backed separatists in eastern Ukraine. The conflict has killed more than 9,800 people in three years.
At the UN, Haley underscored the administration's assurances and reiterated that US sanctions on Russia will remain in place until Crimea is returned to Ukraine.
"The United States thinks it's possible to have a better relationship with Russia," she said.
"But greater cooperation with Russia cannot come at the expense of the security of our European friends and allies." Russia's first deputy UN ambassador, Petr Iliichev, retorted that Ukraine was engaging in "military misadventures" and called on colleagues to "seek reciprocally acceptable solutions to crises in Europe."
Haley also criticised Russia's recent decision to recognize passports issued by separatist authorities in eastern Ukraine as "another direct challenge to efforts to bring peace" there.
Russia characterizes its decision as a humanitarian move to help people who live in rebel-held regions blockaded by Ukrainian nationalists and says it doesn't amount to recognising the rebel regions.