By Martin Finucane and John R. Ellement Globe Staff

A Middlesex Superior Court judge has rejected a lawsuit by an atheist couple and their children who sued the Acton-Boxborough Regional School District and the Acton schools challenging the use of the words “under God” in the Pledge of Allegiance.

Judge S. Jane Haggerty, in a ruling released Friday, said the daily recitation of the pledge with those words did not violate the plaintiffs’ rights under the Massachusetts Constitution, did not violate the school district’s antidiscrimination policy, and did not violate state law.

The plaintiffs, while acknowledging that the children had the right to refuse to participate in the pledge, asserted that the phrase “under God” was a “religious truth” that contradicted their beliefs, Haggerty said.

The defendants argued that the pledge, rather than a religious document or ceremony, is a patriotic exercise and statement of political philosophy, according to the ruling.

The judge observed that the case presents a “familiar dilemma in our pluralistic society — how to balance conflicting interests when one group wants to do something for patriotic reasons that another group finds offensive to its religious (or atheistic) beliefs.”

The judge ruled in her 24-page opinion that the phrase “under God” was not a religious truth.

Citing previous opinions, she said that the daily flag salute and pledge in schools are “clearly designed to inculcate patriotism and to instill a recognition of the blessings conferred by orderly government under the constitutions of the state and nation.”

“The Pledge is a voluntary patriotic exercise, and the inclusion of the phrase ‘under God’ does not convert the exercise into a prayer,” she wrote.