(CNN) Ilhan Omar, a progressive state legislator, will win the Democratic primary in Minnesota's 5th Congressional District, CNN projects.

Backed in her race by Alexandria Ocasio-Cortez, Omar -- who came to the US more than two decades ago as a refugee -- would become the first Somali-American member of Congress if she wins the seat being left behind by Rep. Keith Ellison, who is running for state attorney general, in November.

Omar is also on a path to arrive in Washington, DC, next year with Michigan Democratic House nominee Rashida Tlaib, who is running unopposed in the fall, to become the first Muslim women in Congress. Tlaib campaigned alongside Omar this past weekend, days ahead of the primary.

"We started this campaign to prove people are ready and willing to fight for an America that works for all of us. To every staff member, volunteer, donor, and voter, this win is just as much yours as it is mine," Omar said in a tweet shortly after declaring victory. "Together, we will move our district, state and nation forward."

With the support from the Justice Democrats, the same progressive group that helped bring Ocasio-Cortez into the arena in New York, Omar campaigned on a platform including support for "Medicare for all," abolishing ICE, tuition-free college and raising the minimum wage to $15 an hour. She was also endorsed by Minnesota Gov. Mark Dayton and liberal groups like MoveOn and Democracy for America.

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