WASHINGTON—Mike Pompeo secured his first Democratic senator’s endorsement on Thursday, putting his nomination as the next secretary of state on stronger footing.

Sen. Heidi Heitkamp (D., N.D.) said she would vote to confirm the current Central Intelligence Agency director as the nation’s top diplomat. Another Democrat, Sen. Bill Nelson (D., Fla.), told a local newspaper that he approved of Mr. Pompeo’s recent diplomatic outreach to North Korea and continues to mull whether to support Mr. Pompeo.

Both...